1. CJM Online first
 Kawakami, Yu

Functiontheoretic Properties for the Gauss Maps of Various Classes of Surfaces
We elucidate the geometric background of functiontheoretic properties
for the Gauss maps of
several classes of immersed surfaces in threedimensional space
forms, for example, minimal surfaces in Euclidean threespace, improper affine spheres in the affine threespace, and constant
mean curvature one surfaces and flat surfaces in hyperbolic threespace. To achieve this purpose, we prove an optimal curvature bound
for a specified conformal metric on an open Riemann surface and give some applications. We also provide unicity theorems for
the Gauss maps of these classes of surfaces.
Keywords:Gauss map, minimal surface, constant mean curvature surface, front, ramification, omitted value, the Ahlfors island theorem, unicity theorem. Categories:53C42, 30D35, 30F45, 53A10, 53A15 

2. CJM Online first
 Izumi, Masaki; Morrison, Scott; Penneys, David

Quotients of $A_2 * T_2$
We study unitary quotients of the free product unitary pivotal
category $A_2*T_2$.
We show that such quotients are parametrized by an integer $n\geq
1$ and an $2n$th root of unity $\omega$.
We show that for $n=1,2,3$, there is exactly one quotient and
$\omega=1$.
For $4\leq n\leq 10$, we show that there are no such quotients.
Our methods also apply to quotients of $T_2*T_2$, where we have
a similar result.
The essence of our method is a consistency check on jellyfish
relations.
While we only treat the specific cases of $A_2 * T_2$ and $T_2
* T_2$, we anticipate that our technique can be extended to a
general method for proving nonexistence of planar algebras with
a specified principal graph.
During the preparation of this manuscript, we learnt of Liu's
independent result on composites of $A_3$ and $A_4$ subfactor
planar algebras
(arxiv:1308.5691).
In 1994, BischHaagerup showed that the principal graph of a
composite of $A_3$ and $A_4$ must fit into a certain family,
and Liu has classified all such subfactor planar algebras.
We explain the connection between the quotient categories and
the corresponding composite subfactor planar algebras.
As a corollary of Liu's result, there are no such quotient categories
for $n\geq 4$.
This is an abridged version of
arxiv:1308.5723.
Keywords:pivotal category, free product, quotient, subfactor, intermediate subfactor Category:46L37 

3. CJM Online first
 Barros, Carlos Braga; Rocha, Victor; Souza, Josiney

Lyapunov Stability and Attraction Under Equivariant Maps
Let $M$ and $N$ be admissible Hausdorff topological spaces endowed
with
admissible families of open coverings. Assume that $\mathcal{S}$ is a
semigroup acting on both $M$ and $N$. In this paper we study the behavior of
limit sets, prolongations, prolongational limit sets, attracting sets,
attractors and Lyapunov stable sets (all concepts defined for the action of
the semigroup $\mathcal{S}$) under equivariant maps and semiconjugations
from $M$ to $N$.
Keywords:Lyapunov stability, semigroup actions, generalized flows, equivariant maps, admissible topological spaces Categories:37B25, 37C75, 34C27, 34D05 

4. CJM Online first
 Bonfanti, Matteo Alfonso; van Geemen,

Abelian Surfaces with an Automorphism and Quaternionic Multiplication
We construct one dimensional families of Abelian surfaces with
quaternionic multiplication
which also have an automorphism of order three or four. Using Barth's
description of the moduli space of $(2,4)$polarized Abelian surfaces,
we find the Shimura curve parametrizing these Abelian surfaces in a
specific case.
We explicitly relate these surfaces to the Jacobians of genus two
curves studied by Hashimoto and Murabayashi.
We also describe a (Humbert) surface in Barth's moduli space which
parametrizes Abelian surfaces with real multiplication by
$\mathbf{Z}[\sqrt{2}]$.
Keywords:abelian surfaces, moduli, shimura curves Categories:14K10, 11G10, 14K20 

5. CJM Online first
 Shiozawa, Yuichi

Lower Escape Rate of Symmetric Jumpdiffusion Processes
We establish an integral test on the lower escape rate
of symmetric jumpdiffusion processes generated by regular Dirichlet
forms.
Using this test, we can find the speed of particles escaping
to infinity.
We apply this test to symmetric jump processes of variable order. We also derive the upper and lower escape rates of time changed
processes
by using those of underlying processes.
Keywords:lower escape rate, Dirichlet form, Markov process, time change Categories:60G17, 31C25, 60J25 

6. CJM Online first
 Martins, Luciana de Fátima; Saji, Kentaro

Geometric invariants of cuspidal edges
We give a normal form of the cuspidal edge
which uses only diffeomorphisms on the source
and isometries on the target.
Using this normal form, we study differential
geometric invariants of
cuspidal edges which determine them up to order three.
We also
clarify relations between these invariants.
Keywords:cuspidal edge, curvature, wave fronts Categories:57R45, 53A05, 53A55 

7. CJM 2015 (vol 67 pp. 481)
 an Huef, Astrid; Archbold, Robert John

The C*algebras of Compact Transformation Groups
We investigate the representation theory of the
crossedproduct $C^*$algebra associated to a compact group $G$
acting on a locally compact space $X$ when the stability subgroups
vary discontinuously.
Our main result applies when $G$ has a principal stability subgroup or
$X$ is locally of finite $G$orbit type. Then the upper multiplicity
of the representation of the crossed product induced from an
irreducible representation $V$ of a stability subgroup is obtained by
restricting $V$ to a certain closed subgroup of the stability subgroup
and taking the maximum of the multiplicities of the irreducible
summands occurring in the restriction of $V$. As a corollary we obtain
that when the trivial subgroup is a principal stability subgroup, the
crossed product is a Fell algebra if and only if every stability
subgroup is abelian. A second corollary is that the $C^*$algebra of
the motion group $\mathbb{R}^n\rtimes \operatorname{SO}(n)$ is a Fell algebra. This uses
the classical branching theorem for the special orthogonal group
$\operatorname{SO}(n)$ with respect to $\operatorname{SO}(n1)$. Since proper transformation
groups are locally induced from the actions of compact groups, we
describe how some of our results can be extended to transformation
groups that are locally proper.
Keywords:compact transformation group, proper action, spectrum of a C*algebra, multiplicity of a representation, crossedproduct C*algebra, continuoustrace C*algebra, Fell algebra Categories:46L05, 46L55 

8. CJM 2015 (vol 67 pp. 696)
 Zhang, Tong

Geography of Irregular Gorenstein 3folds
In this paper, we study the explicit geography problem of irregular Gorenstein minimal 3folds of general type. We generalize the classical NoetherCastelnuovo type inequalities for irregular surfaces to irregular 3folds according to the Albanese dimension.
Keywords:3fold, geography, irregular variety Category:14J30 

9. CJM Online first
 Aluffi, Paolo; Faber, Eleonore

Chern classes of splayed intersections
We generalize the Chern class relation for the transversal intersection
of two nonsingular
varieties to a relation for possibly singular varieties, under
a splayedness assumption.
We show that the relation for the ChernSchwartzMacPherson classes
holds for two splayed hypersurfaces in a nonsingular variety,
and under a `strong splayedness' assumption for more
general subschemes. Moreover, the relation is shown to hold for
the ChernFulton classes
of any two splayed subschemes.
The main tool is a formula for Segre classes of splayed
subschemes. We also discuss the Chern class relation under the
assumption that one of the
varieties is a general very ample divisor.
Keywords:splayed intersection, ChernSchwartzMacPherson class, ChernFulton class, splayed blowup, Segre class Categories:14C17, 14J17 

10. CJM Online first
 Jaffe, Ethan Y.

Pathological phenomena in DenjoyCarleman classes
Let $\mathcal{C}^M$ denote a DenjoyCarleman class of $\mathcal{C}^\infty$
functions (for a given logarithmicallyconvex sequence $M = (M_n)$).
We construct: (1) a function in $\mathcal{C}^M((1,1))$ which
is nowhere in any smaller class; (2) a function on $\mathbb{R}$ which
is formally $\mathcal{C}^M$ at every point, but not in
$\mathcal{C}^M(\mathbb{R})$;
(3) (under the assumption of quasianalyticity) a smooth function
on $\mathbb{R}^p$ ($p \geq 2$) which is $\mathcal{C}^M$ on every $\mathcal{C}^M$
curve, but not in $\mathcal{C}^M(\mathbb{R}^p)$.
Keywords:DenjoyCarleman classes, quasianalytic functions, quasianalytic curve, arcquasianalytic Category:26E10 

11. CJM Online first
 Carey, Alan L; Gayral, Victor; Phillips, John; Rennie, Adam; Sukochev, Fedor

Spectral flow for nonunital spectral triples
We prove two results about nonunital index theory left open in a
previous paper. The
first is that the spectral triple arising from an action of the reals on a $C^*$algebra with invariant trace
satisfies the hypotheses of the nonunital local index formula. The second result concerns the meaning of spectral flow in the nonunital case. For the special case of paths
arising from the odd
index pairing for smooth spectral triples in the nonunital setting we are able to connect with earlier approaches to the analytic definition of spectral flow.
Keywords:spectral triple, spectral flow, local index theorem Category:46H30 

12. CJM 2015 (vol 67 pp. 597)
 Drappeau, Sary

Sommes friables d'exponentielles et applications
An integer is said to be $y$friable if its greatest prime factor is less than $y$.
In this paper, we obtain estimates for exponential sums
over $y$friable numbers up to $x$ which are nontrivial
when $y \geq \exp\{c \sqrt{\log x} \log \log x\}$. As a consequence,
we obtain an asymptotic formula for the
number of $y$friable solutions to the equation $a+b=c$ which is valid
unconditionnally under the same assumption.
We use a contour integration argument based on the saddle point
method, as developped in the context of friable numbers by Hildebrand
and Tenenbaum,
and used by Lagarias, Soundararajan and Harper to study exponential and character sums over friable numbers.
Keywords:thÃ©orie analytique des nombres, entiers friables, mÃ©thode du col Categories:12N25, 11L07 

13. CJM Online first
 Zhang, Junqiang; Cao, Jun; Jiang, Renjin; Yang, Dachun

Nontangential Maximal Function Characterizations of Hardy Spaces Associated with Degenerate Elliptic Operators
Let $w$ be either in the Muckenhoupt class of $A_2(\mathbb{R}^n)$ weights
or in the class of $QC(\mathbb{R}^n)$ weights, and
$L_w:=w^{1}\mathop{\mathrm{div}}(A\nabla)$
the degenerate elliptic operator on the Euclidean space $\mathbb{R}^n$,
$n\ge 2$. In this article, the authors establish the nontangential
maximal function characterization
of the Hardy space $H_{L_w}^p(\mathbb{R}^n)$ associated with $L_w$ for
$p\in (0,1]$ and, when $p\in (\frac{n}{n+1},1]$ and
$w\in A_{q_0}(\mathbb{R}^n)$ with $q_0\in[1,\frac{p(n+1)}n)$,
the authors prove that the associated Riesz transform $\nabla L_w^{1/2}$
is bounded from $H_{L_w}^p(\mathbb{R}^n)$ to the weighted classical
Hardy space $H_w^p(\mathbb{R}^n)$.
Keywords:degenerate elliptic operator, Hardy space, square function, maximal function, molecule, Riesz transform Categories:42B30, 42B35, 35J70 

14. CJM Online first
 Stange, Katherine E.

Integral Points on Elliptic Curves and Explicit Valuations of Division Polynomials
Assuming Lang's conjectured lower bound on the heights of nontorsion
points on an elliptic curve, we show that there exists an absolute
constant $C$ such that for any elliptic curve $E/\mathbb{Q}$ and nontorsion
point $P \in E(\mathbb{Q})$, there is at most one integral multiple
$[n]P$ such that $n \gt C$. The proof is a modification of a proof
of Ingram giving an unconditional but not uniform bound. The
new ingredient is a collection of explicit formulae for the
sequence $v(\Psi_n)$ of valuations of the division polynomials.
For $P$ of nonsingular reduction, such sequences are already
well described in most cases, but for $P$ of singular reduction,
we are led to define a new class of sequences called \emph{elliptic
troublemaker sequences}, which measure the failure of the NÃ©ron
local height to be quadratic. As a corollary in the spirit of
a conjecture of Lang and Hall, we obtain a uniform upper bound
on $\widehat{h}(P)/h(E)$ for integer points having two large
integral multiples.
Keywords:elliptic divisibility sequence, Lang's conjecture, height functions Categories:11G05, 11G07, 11D25, 11B37, 11B39, 11Y55, 11G50, 11H52 

15. CJM Online first
 Cojocaru, Alina Carmen; Shulman, Andrew Michael

The Distribution of the First Elementary Divisor of the Reductions of a Generic Drinfeld Module of Arbitrary Rank
Let $\psi$ be a generic Drinfeld module of rank $r \geq 2$. We study
the first elementary divisor
$d_{1, \wp}(\psi)$ of the reduction of $\psi$ modulo a prime $\wp$, as $\wp$ varies.
In particular, we prove the existence of the density of the primes $\wp$ for which $d_{1, \wp} (\psi)$ is fixed. For $r = 2$, we also study the second elementary divisor (the exponent) of the reduction of $\psi$ modulo $\wp$
and prove that, on average, it has a large norm. Our work is motivated by the study of J.P. Serre of an elliptic curve analogue of Artin's Primitive Root Conjecture, and, moreover, by refinements to Serre's study developed by the first author and M.R. Murty.
Keywords:Drinfeld modules, density theorems Categories:11R45, 11G09, 11R58 

16. CJM Online first
 Sadykov, Rustam

The Weak bprinciple: Mumford Conjecture
In this note we introduce and study a new class of maps called
oriented colored broken submersions. This is the simplest class
of maps that satisfies a version of the bprinciple and in dimension
$2$ approximates the class of oriented submersions well in the
sense that
every oriented colored broken submersion of dimension $2$ to
a closed simply connected manifold is bordant to a submersion.
We show that the MadsenWeiss theorem (the standard Mumford Conjecture)
fits a general setting of the bprinciple. Namely, a version
of the bprinciple for
oriented colored broken submersions together with the Harer
stability theorem and MillerMorita theorem implies the MadsenWeiss
theorem.
Keywords:generalized cohomology theories, fold singularities, hprinciple, infinite loop spaces Categories:55N20, 53C23 

17. CJM Online first
 Kaniuth, Eberhard

The BochnerSchoenbergEberlein property and spectral synthesis for certain Banach algebra products
Associated with two commutative Banach algebras $A$ and $B$ and
a character $\theta$ of $B$ is a certain Banach algebra product
$A\times_\theta B$, which is a splitting extension of $B$ by
$A$. We investigate two topics for the algebra $A\times_\theta
B$ in relation to the corresponding ones of $A$ and $B$. The
first one is the BochnerSchoenbergEberlein property and the
algebra of BochnerSchoenbergEberlein functions on the spectrum,
whereas the second one concerns the wide range of spectral synthesis
problems for $A\times_\theta B$.
Keywords:commutative Banach algebra, splitting extension, Gelfand spectrum, set of synthesis, weak spectral set, multiplier algebra, BSEalgebra, BSEfunction Categories:46J10, 46J25, 43A30, 43A45 

18. CJM Online first
 Charlesworth, Ian; Nelson, Brent; Skoufranis, Paul

On twofaced families of noncommutative random variables
We demonstrate that the notions of bifree independence and combinatorialbifree
independence of twofaced families are equivalent using a diagrammatic
view of binoncrossing partitions.
These diagrams produce an operator model on a Fock space suitable
for representing any twofaced family of noncommutative random
variables.
Furthermore, using a Kreweras complement on binoncrossing partitions
we establish the expected formulas for the multiplicative convolution
of a bifree pair of twofaced families.
Keywords:free probability, operator algebras, bifree Category:46L54 

19. CJM Online first
 Carcamo, Cristian; Vidal, Claudio

Stability of Equilibrium Solutions in Planar Hamiltonian Difference Systems
In this paper, we study the stability in the Lyapunov sense of the
equilibrium solutions of discrete or difference Hamiltonian systems
in the plane. First, we perform a detailed study of linear
Hamiltonian systems as a function of the parameters, in particular
we analyze the regular and the degenerate cases. Next, we give a
detailed study of the normal form associated with the linear
Hamiltonian system. At the same time we obtain the conditions under
which we can get stability (in linear approximation) of the
equilibrium solution, classifying all the possible phase diagrams as
a function of the parameters. After that, we study the stability of
the equilibrium solutions of the first order difference system in
the plane associated to mechanical Hamiltonian system and
Hamiltonian system defined by cubic polynomials. Finally, important
differences with the continuous case are pointed out.
Keywords:difference equations, Hamiltonian systems, stability in the Lyapunov sense Categories:34D20, 34E10 

20. CJM Online first
 Amini, Massoud; Elliott, George A.; Golestani, Nasser

The Category of Bratteli Diagrams
A category structure for Bratteli diagrams is proposed and a
functor from
the category of AF algebras to the category of Bratteli diagrams
is
constructed. Since isomorphism of Bratteli diagrams in this
category coincides
with Bratteli's notion of equivalence, we obtain in particular
a functorial formulation of Bratteli's
classification of AF algebras (and at the same time, of Glimm's
classification of UHF~algebras).
It is shown that the three approaches
to classification of AF~algebras, namely, through Bratteli diagrams,
Ktheory, and
abstract classifying categories, are essentially the same
from a categorical point of view.
Keywords:C$^{*}$algebra, category, functor, AF algebra, dimension group, Bratteli diagram Categories:46L05, 46L35, 46M15 

21. CJM Online first
 Takeda, Shuichiro

Metaplectic Tensor Products for Automorphic Representation of $\widetilde{GL}(r)$
Let $M=\operatorname{GL}_{r_1}\times\cdots\times\operatorname{GL}_{r_k}\subseteq\operatorname{GL}_r$ be a Levi
subgroup of $\operatorname{GL}_r$, where $r=r_1+\cdots+r_k$, and $\widetilde{M}$ its metaplectic preimage
in the $n$fold metaplectic cover $\widetilde{\operatorname{GL}}_r$ of $\operatorname{GL}_r$. For automorphic
representations $\pi_1,\dots,\pi_k$ of $\widetilde{\operatorname{GL}}_{r_1}(\mathbb{A}),\dots,\widetilde{\operatorname{GL}}_{r_k}(\mathbb{A})$,
we construct (under a certain
technical assumption, which is always satisfied when $n=2$) an
automorphic representation $\pi$
of $\widetilde{M}(\mathbb{A})$ which can be considered as the ``tensor product'' of the
representations $\pi_1,\dots,\pi_k$. This is
the global analogue of the metaplectic tensor product
defined by P. Mezo in the sense that locally at each place $v$,
$\pi_v$ is equivalent to the local metaplectic tensor product of
$\pi_{1,v},\dots,\pi_{k,v}$ defined by Mezo. Then we show that if all
of $\pi_i$ are cuspidal (resp. squareintegrable modulo center), then
the metaplectic tensor product is cuspidal (resp. squareintegrable
modulo center). We also show that (both
locally and globally) the metaplectic tensor product behaves in the
expected way under the action of a Weyl group element, and show the
compatibility with parabolic inductions.
Keywords:automorphic forms, representations of covering groups Category:11F70 

22. CJM Online first
 Pan, Ivan Edgardo; Simis, Aron

Cremona Maps of de JonquiÃ¨res Type
This paper is concerned with suitable generalizations of a plane de
JonquiÃ¨res map to higher dimensional space
$\mathbb{P}^n$ with $n\geq 3$.
For each given point of $\mathbb{P}^n$ there is a subgroup of the entire
Cremona group of dimension $n$
consisting of such maps.
One studies both geometric and grouptheoretical properties of this notion.
In the case where $n=3$ one describes an explicit set of generators of
the group and gives a homological characterization
of a basic subgroup thereof.
Keywords:Cremona map, de JonquiÃ¨res map, Cremona group, minimal free resolution Categories:14E05, 13D02, 13H10, 14E07, 14M05, 14M25 

23. CJM 2014 (vol 67 pp. 241)
 Agler, Jim; McCarthy,

Global Holomorphic Functions in Several Noncommuting Variables
We define a free holomorphic function to be a function
that is locally, with respect to the free topology, a bounded
ncfunction.
We prove that free holomorphic functions are the functions that
are locally uniformly approximable
by free polynomials. We prove a realization formula and an OkaWeil
theorem for free analytic functions.
Keywords:noncommutative analysis, free holomorphic functions Category:15A54 

24. CJM 2014 (vol 67 pp. 404)
 Hua, Jiajie; Lin, Huaxin

Rotation Algebras and the Exel Trace Formula
We found that if $u$ and $v$ are any two unitaries in
a unital $C^*$algebra with $\uvvu\\lt 2$ and $uvu^*v^*$ commutes with
$u$ and $v,$ then the $C^*$subalgebra $A_{u,v}$ generated by $u$ and
$v$ is isomorphic to a quotient of some rotation algebra $A_\theta$
provided that $A_{u,v}$ has a unique tracial state.
We also found that the Exel trace formula holds in any unital
$C^*$algebra.
Let $\theta\in (1/2, 1/2)$ be a real number. We prove the
following:
For any $\epsilon\gt 0,$ there exists $\delta\gt 0$ satisfying the following:
if $u$ and $v$ are two unitaries in any unital simple $C^*$algebra
$A$ with tracial rank zero such that
\[
\uve^{2\pi i\theta}vu\\lt \delta
\text{ and }
{1\over{2\pi i}}\tau(\log(uvu^*v^*))=\theta,
\]
for all tracial state $\tau$ of $A,$ then there exists a pair
of unitaries $\tilde{u}$ and $\tilde{v}$ in $A$
such that
\[
\tilde{u}\tilde{v}=e^{2\pi i\theta} \tilde{v}\tilde{u},\,\,
\u\tilde{u}\\lt \epsilon
\text{ and }
\v\tilde{v}\\lt \epsilon.
\]
Keywords:rotation algebras, Exel trace formula Category:46L05 

25. CJM 2014 (vol 67 pp. 152)
 Lescop, Christine

On Homotopy Invariants of Combings of Threemanifolds
Combings of compact, oriented $3$dimensional manifolds $M$ are
homotopy classes of nowhere vanishing vector fields.
The Euler class of the normal bundle is an invariant of the combing,
and it only depends on the underlying Spin$^c$structure. A combing
is called torsion
if this Euler class is a torsion element of $H^2(M;\mathbb Z)$. Gompf
introduced a $\mathbb Q$valued invariant $\theta_G$ of torsion combings
on closed $3$manifolds, and he showed that $\theta_G$ distinguishes
all torsion combings with the same Spin$^c$structure.
We give an alternative definition for $\theta_G$ and we express
its variation as a linking number. We define a similar invariant
$p_1$ of combings for manifolds bounded by $S^2$. We relate $p_1$
to the $\Theta$invariant, which is the simplest configuration
space integral invariant of rational homology $3$balls, by the
formula $\Theta=\frac14p_1 + 6 \lambda(\hat{M})$ where $\lambda$
is the CassonWalker invariant.
The article also includes a selfcontained presentation of combings
for $3$manifolds.
Keywords:Spin$^c$structure, nowhere zero vector fields, first Pontrjagin class, Euler class, Heegaard Floer homology grading, Gompf invariant, Theta invariant, CassonWalker invariant, perturbative expansion of ChernSimons theory, configuration space integrals Categories:57M27, 57R20, 57N10 
