Expand all Collapse all | Results 51 - 75 of 440 |
51. CMB 2013 (vol 57 pp. 870)
A Short Note on Short Pants It is a theorem of Bers that any closed hyperbolic surface admits a pants decomposition consisting of curves of bounded length where the bound only depends on the topology of the surface. The question of the quantification of the optimal constants has been well studied and the best upper bounds to date are linear in genus, a theorem of Buser and SeppÃ¤lÃ¤. The goal of this note is to give a short proof of a linear upper bound which slightly improve the best known bound.
Keywords:hyperbolic surfaces, geodesics, pants decompositions Categories:30F10, 32G15, 53C22 |
52. CMB 2013 (vol 57 pp. 845)
Factorisation of Two-variable $p$-adic $L$-functions Let $f$ be a modular form which is non-ordinary at $p$. Loeffler has
recently constructed four two-variable $p$-adic $L$-functions
associated to $f$. In the case where $a_p=0$, he showed that, as in
the one-variable case, Pollack's plus and minus splitting applies to
these new objects. In this article, we show that such a splitting can
be generalised to the case where $a_p\ne0$ using Sprung's logarithmic
matrix.
Keywords:modular forms, p-adic L-functions, supersingular primes Categories:11S40, 11S80 |
53. CMB 2013 (vol 57 pp. 463)
Constructive Proof of Carpenter's Theorem We give a constructive proof of Carpenter's Theorem due to Kadison.
Unlike the original proof our approach also yields the
real case of this theorem.
Keywords:diagonals of projections, the Schur-Horn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory Categories:42C15, 47B15, 46C05 |
54. CMB 2013 (vol 57 pp. 585)
Short Probabilistic Proof of the Brascamp-Lieb and Barthe Theorems We give a short proof of the Brascamp-Lieb theorem, which asserts that
a certain general form of Young's convolution inequality is saturated
by Gaussian functions. The argument is inspired by Borell's stochastic
proof of the PrÃ©kopa-Leindler inequality and applies also to the
reversed Brascamp-Lieb inequality, due to Barthe.
Keywords:functional inequalities, Brownian motion Categories:39B62, 60J65 |
55. CMB 2013 (vol 57 pp. 526)
On $3$-manifolds with Torus or Klein Bottle Category Two A subset $W$ of a closed manifold $M$ is $K$-contractible, where $K$
is a torus or Kleinbottle, if the inclusion $W\rightarrow M$ factors
homotopically through a map to $K$. The image of $\pi_1 (W)$ (for any
base point) is a subgroup of $\pi_1 (M)$ that is isomorphic to a
subgroup of a quotient group of $\pi_1 (K)$. Subsets of $M$ with this
latter property are called $\mathcal{G}_K$-contractible. We obtain a
list of the closed $3$-manifolds that can be covered by two open
$\mathcal{G}_K$-contractible subsets. This is applied to obtain a list
of the possible closed prime $3$-manifolds that can be covered by two
open $K$-contractible subsets.
Keywords:Lusternik--Schnirelmann category, coverings of $3$-manifolds by open $K$-contractible sets Categories:57N10, 55M30, 57M27, 57N16 |
56. CMB 2013 (vol 57 pp. 119)
Splitting Families and Complete Separability We answer a question from Raghavan and SteprÄns
by showing that $\mathfrak{s} = {\mathfrak{s}}_{\omega, \omega}$. Then we use this to construct a completely separable maximal almost disjoint family under $\mathfrak{s} \leq \mathfrak{a}$, partially answering a question of Shelah.
Keywords:maximal almost disjoint family, cardinal invariants Categories:03E05, 03E17, 03E65 |
57. CMB Online first
Left-orderable fundamental group and Dehn surgery on the knot $5_2$ We show that the resulting manifold by $r$-surgery on the knot $5_2$, which is
the two-bridge knot corresponding to the rational number $3/7$, has left-orderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:left-ordering, Dehn surgery Categories:57M25, 06F15 |
58. CMB Online first
Left-orderable fundamental group and Dehn surgery on the knot $5_2$ We show that the resulting manifold by $r$-surgery on the knot $5_2$, which is
the two-bridge knot corresponding to the rational number $3/7$, has left-orderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:left-ordering, Dehn surgery Categories:57M25, 06F15 |
59. CMB 2013 (vol 57 pp. 245)
Assouad-Nagata Dimension of Wreath Products of Groups Consider the wreath product $H\wr G$, where $H\ne 1$ is finite and $G$ is finitely generated.
We show that the Assouad-Nagata dimension $\dim_{AN}(H\wr G)$ of $H\wr G$
depends on the growth of $G$ as follows:
\par If the growth of $G$ is not bounded by a linear function, then $\dim_{AN}(H\wr G)=\infty$,
otherwise $\dim_{AN}(H\wr G)=\dim_{AN}(G)\leq 1$.
Keywords:Assouad-Nagata dimension, asymptotic dimension, wreath product, growth of groups Categories:54F45, 55M10, 54C65 |
60. CMB 2013 (vol 57 pp. 439)
The Fixed Point Locus of the Verschiebung on $\mathcal{M}_X(2, 0)$ for Genus-2 Curves $X$ in Charateristic $2$ |
The Fixed Point Locus of the Verschiebung on $\mathcal{M}_X(2, 0)$ for Genus-2 Curves $X$ in Charateristic $2$ We prove that for every ordinary genus-$2$ curve $X$ over a finite
field $\kappa$ of characteristic $2$ with
$\textrm{Aut}(X/\kappa)=\mathbb{Z}/2\mathbb{Z} \times S_3$, there exist
$\textrm{SL}(2,\kappa[\![s]\!])$-representations of $\pi_1(X)$ such
that the image of $\pi_1(\overline{X})$ is infinite. This result
produces a family of examples similar to Laszlo's counterexample
to de Jong's question regarding the finiteness of the geometric
monodromy of representations of the fundamental group.
Keywords:vector bundle, Frobenius pullback, representation, etale fundamental group Categories:14H60, 14D05, 14G15 |
61. CMB 2013 (vol 57 pp. 381)
On Complex Explicit Formulae Connected with the MÃ¶bius Function of an Elliptic Curve We study analytic properties function $m(z, E)$, which is defined on the upper half-plane as an integral from the shifted $L$-function of an elliptic curve. We show that $m(z, E)$ analytically continues to a meromorphic function on the whole complex plane and satisfies certain functional equation. Moreover, we give explicit formula for $m(z, E)$ in the strip $|\Im{z}|\lt 2\pi$.
Keywords:L-function, MÃ¶bius function, explicit formulae, elliptic curve Categories:11M36, 11G40 |
62. CMB 2013 (vol 57 pp. 310)
Left-orderable Fundamental Group and Dehn Surgery on the Knot $5_2$ We show that the resulting manifold by $r$-surgery on the knot $5_2$, which is
the two-bridge knot corresponding to the rational number $3/7$, has left-orderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:left-ordering, Dehn surgery Categories:57M25, 06F15 |
63. CMB 2013 (vol 57 pp. 821)
Real Hypersurfaces in Complex Two-Plane Grassmannians with Reeb Parallel Structure Jacobi Operator In this paper we give a characterization of a real hypersurface of
Type~$(A)$ in complex two-plane Grassmannians ${ { {G_2({\mathbb
C}^{m+2})} } }$, which means a
tube over a totally geodesic $G_{2}(\mathbb C^{m+1})$ in
${G_2({\mathbb C}^{m+2})}$, by
the Reeb parallel structure Jacobi operator ${\nabla}_{\xi}R_{\xi}=0$.
Keywords:real hypersurfaces, complex two-plane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator Categories:53C40, 53C15 |
64. CMB 2013 (vol 57 pp. 506)
On Braided and Ribbon Unitary Fusion Categories We prove that every braiding over a unitary fusion category is
unitary and every unitary braided fusion category admits a unique
unitary ribbon structure.
Keywords:fusion categories, braided categories, modular categories Categories:20F36, 16W30, 18D10 |
65. CMB 2013 (vol 57 pp. 401)
Curvature of $K$-contact Semi-Riemannian Manifolds In this paper we characterize $K$-contact semi-Riemannian manifolds
and Sasakian semi-Riemannian manifolds in terms of
curvature. Moreover, we show that any conformally flat $K$-contact
semi-Riemannian manifold is Sasakian and of constant sectional
curvature $\kappa=\varepsilon$, where $\varepsilon =\pm 1$ denotes
the causal character of the Reeb vector field. Finally, we give some
results about the curvature of a $K$-contact Lorentzian manifold.
Keywords:contact semi-Riemannian structures, $K$-contact structures, conformally flat manifolds, Einstein Lorentzian-Sasaki manifolds Categories:53C50, 53C25, 53B30 |
66. CMB 2013 (vol 57 pp. 254)
On Parseval Wavelet Frames with Two or Three Generators via the Unitary Extension Principle The unitary extension principle (UEP) by Ron and Shen yields a
sufficient condition for the construction of Parseval wavelet frames with
multiple generators. In this paper we characterize the UEP-type wavelet systems that
can be extended to a Parseval wavelet frame by adding just one UEP-type wavelet
system. We derive a condition that is necessary for the extension of a UEP-type
wavelet system to any Parseval wavelet frame with any number of generators, and
prove that this condition is also sufficient to ensure that an extension
with just two generators is possible.
Keywords:Bessel sequences, frames, extension of wavelet Bessel system to tight frame, wavelet systems, unitary extension principle Categories:42C15, 42C40 |
67. CMB 2013 (vol 57 pp. 449)
ZL-amenability Constants of Finite Groups with Two Character Degrees We calculate the exact amenability constant of the centre of
$\ell^1(G)$ when $G$ is one of the following classes of finite group:
dihedral; extraspecial; or Frobenius with abelian complement and
kernel. This is done using a formula which applies to all finite
groups with two character degrees. In passing, we answer in the
negative a question raised in work of the third author with Azimifard
and Spronk (J. Funct. Anal. 2009).
Keywords:center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups Categories:43A20, 20C15 |
68. CMB 2013 (vol 57 pp. 141)
Size, Order, and Connected Domination We give a sharp upper bound on the size of a
triangle-free graph of a given order and connected domination. Our
bound, apart from
strengthening an old classical theorem of Mantel and of
TurÃ¡n , improves on a theorem of Sanchis.
Further, as corollaries, we settle a long standing
conjecture of Graffiti on the leaf number and local independence for
triangle-free graphs and answer a question of Griggs, Kleitman and
Shastri on a lower bound of the leaf number in
triangle-free graphs.
Keywords:size, connected domination, local independence number, leaf number Category:05C69 |
69. CMB 2013 (vol 57 pp. 125)
Camina Triples In this paper, we study Camina triples. Camina triples are a
generalization of Camina pairs. Camina pairs were first introduced
in 1978 by A .R. Camina.
Camina's work
was inspired by the study of Frobenius groups. We
show that if $(G,N,M)$ is a Camina triple, then either $G/N$ is a
$p$-group, or $M$ is abelian, or $M$ has a non-trivial nilpotent or
Frobenius quotient.
Keywords:Camina triples, Camina pairs, nilpotent groups, vanishing off subgroup, irreducible characters, solvable groups Category:20D15 |
70. CMB 2013 (vol 57 pp. 357)
Representation Equivalent Bieberbach Groups and Strongly Isospectral Flat Manifolds Let $\Gamma_1$ and $\Gamma_2$ be Bieberbach groups contained in the
full isometry group $G$ of $\mathbb{R}^n$.
We prove that if the compact flat manifolds $\Gamma_1\backslash\mathbb{R}^n$ and
$\Gamma_2\backslash\mathbb{R}^n$ are strongly isospectral then the Bieberbach groups
$\Gamma_1$ and $\Gamma_2$ are representation equivalent, that is, the
right regular representations $L^2(\Gamma_1\backslash G)$ and
$L^2(\Gamma_2\backslash G)$ are unitarily equivalent.
Keywords:representation equivalent, strongly isospectrality, compact flat manifolds Categories:58J53, 22D10 |
71. CMB 2013 (vol 57 pp. 335)
Alexandroff Manifolds and Homogeneous Continua ny homogeneous,
metric $ANR$-continuum is a $V^n_G$-continuum provided $\dim_GX=n\geq
1$ and $\check{H}^n(X;G)\neq 0$, where $G$ is a principal ideal
domain.
This implies that any homogeneous $n$-dimensional metric $ANR$-continuum is a $V^n$-continuum in the sense of Alexandroff.
We also prove that any finite-dimensional homogeneous metric continuum
$X$, satisfying $\check{H}^n(X;G)\neq 0$ for some group $G$ and $n\geq
1$, cannot be separated by
a compactum $K$ with $\check{H}^{n-1}(K;G)=0$ and $\dim_G K\leq
n-1$. This provides a partial answer to a question of
Kallipoliti-Papasoglu
whether any two-dimensional homogeneous Peano continuum cannot be separated by arcs.
Keywords:Cantor manifold, cohomological dimension, cohomology groups, homogeneous compactum, separator, $V^n$-continuum Categories:54F45, 54F15 |
72. CMB 2013 (vol 57 pp. 364)
How Lipschitz Functions Characterize the Underlying Metric Spaces Let $X, Y$ be metric spaces and $E, F$ be Banach spaces. Suppose that
both $X,Y$ are realcompact, or both $E,F$ are realcompact.
The zero set of a vector-valued function $f$ is denoted by $z(f)$.
A linear bijection $T$ between local or generalized Lipschitz vector-valued function spaces
is said to preserve zero-set containments or nonvanishing functions
if
\[z(f)\subseteq z(g)\quad\Longleftrightarrow\quad z(Tf)\subseteq z(Tg),\]
or
\[z(f) = \emptyset\quad \Longleftrightarrow\quad z(Tf)=\emptyset,\]
respectively.
Every zero-set containment preserver, and every nonvanishing function preserver when
$\dim E =\dim F\lt +\infty$, is a weighted composition operator
$(Tf)(y)=J_y(f(\tau(y)))$.
We show that the map $\tau\colon Y\to X$ is a locally (little) Lipschitz homeomorphism.
Keywords:(generalized, locally, little) Lipschitz functions, zero-set containment preservers, biseparating maps Categories:46E40, 54D60, 46E15 |
73. CMB 2013 (vol 56 pp. 729)
The Orthonormal Dilation Property for Abstract Parseval Wavelet Frames In this work we introduce a class of discrete groups containing
subgroups of abstract translations and dilations, respectively. A
variety of wavelet systems can appear as $\pi(\Gamma)\psi$, where $\pi$ is
a unitary representation of a wavelet group and $\Gamma$ is the abstract
pseudo-lattice $\Gamma$. We prove a condition in order that a Parseval
frame $\pi(\Gamma)\psi$ can be dilated to an orthonormal basis of the
form $\tau(\Gamma)\Psi$ where $\tau$ is a super-representation of
$\pi$. For a subclass of groups that includes the case where the
translation subgroup is Heisenberg, we show that this condition
always holds, and we cite familiar examples as applications.
Keywords:frame, dilation, wavelet, Baumslag-Solitar group, shearlet Categories:43A65, 42C40, 42C15 |
74. CMB 2013 (vol 56 pp. 449)
The $f$-Chromatic Index of a Graph Whose $f$-Core has Maximum Degree $2$ Let $G$ be a graph. The minimum number of colors needed to color the edges of
$G$ is called the chromatic index of $G$ and is denoted by $\chi'(G)$.
It is well-known that $\Delta(G) \leq \chi'(G) \leq \Delta(G)+1$, for any
graph $G$, where $\Delta(G)$ denotes the maximum degree of $G$. A graph $G$ is said to be
Class $1$ if $\chi'(G) = \Delta(G)$ and Class $2$ if
$\chi'(G) = \Delta(G) + 1$. Also, $G_\Delta$ is the induced subgraph on all vertices of degree $\Delta(G)$.
Let $f:V(G)\rightarrow \mathbb{N}$ be a function.
An $f$-coloring of a graph $G$ is a coloring of the edges
of $E(G)$ such that each color appears at each vertex $v\in V(G)$ at
most $f (v)$ times. The minimum number of colors needed
to $f$-color $G$ is called the $f$-chromatic index of $G$ and
is denoted by $\chi'_{f}(G)$. It was shown that for every graph $G$, $\Delta_{f}(G)\le \chi'_{f}(G)\le \Delta_{f}(G)+1$, where $\Delta_{f}(G)=\max_{v\in V(G)} \big\lceil \frac{d_G(v)}{f(v)}\big\rceil$. A graph $G$ is said to be $f$-Class $1$ if $\chi'_{f}(G)=\Delta_{f}(G)$, and $f$-Class $2$, otherwise. Also, $G_{\Delta_f}$ is the induced subgraph of $G$ on $\{v\in V(G):\,\frac{d_G(v)}{f(v)}=\Delta_{f}(G)\}$.
Hilton and Zhao showed that if $G_{\Delta}$ has maximum degree two and $G$ is Class $2$, then $G$ is critical, $G_{\Delta}$ is a disjoint union of cycles and $\delta(G)=\Delta(G)-1$, where $\delta(G)$ denotes the minimum degree of $G$, respectively. In this paper, we generalize this theorem to $f$-coloring of graphs. Also, we determine the $f$-chromatic index of a connected graph $G$ with $|G_{\Delta_f}|\le 4$.
Keywords:$f$-coloring, $f$-Core, $f$-Class $1$ Categories:05C15, 05C38 |
75. CMB Online first
An Explicit Formula for the Generalized Cyclic Shuffle Map We provide an explicit formula for the generalized cyclic shuffle map for cylindrical modules.
Using this formula we give a combinatorial proof of the generalized
cyclic Eilenberg-Zilber theorem.
Keywords:generalized Cyclic shuffle map, Cylindrical module, Eilenberg-Zilber theorem, Cyclic homology Categories:19D55, 05E45 |