76. CMB 2014 (vol 58 pp. 44)
77. CMB 2014 (vol 58 pp. 110)
 Kamalov, F.

Property T and Amenable Transformation Group $C^*$algebras
It is well known that a discrete group which is both amenable and
has Kazhdan's Property T must be finite. In this note we generalize
the above statement to the case of transformation groups. We show
that if $G$ is a discrete amenable group acting on a compact
Hausdorff space $X$, then the transformation group $C^*$algebra
$C^*(X, G)$ has Property T if and only if both $X$ and $G$ are finite. Our
approach does not rely on the use of tracial states on $C^*(X, G)$.
Keywords:Property T, $C^*$algebras, transformation group, amenable Categories:46L55, 46L05 

78. CMB 2014 (vol 57 pp. 721)
 Bruillard, Paul; Galindo, César; Hong, SeungMoon; Kashina, Yevgenia; Naidu, Deepak; Natale, Sonia; Plavnik, Julia Yael; Rowell, Eric C.

Classification of Integral Modular Categories of FrobeniusPerron Dimension $pq^4$ and $p^2q^2$
We classify integral modular categories of dimension $pq^4$ and $p^2q^2$,
where
$p$ and $q$ are distinct primes. We show that such categories are always
grouptheoretical except for categories of dimension $4q^2$.
In these cases there are
wellknown examples of nongrouptheoretical categories, coming from
centers of
TambaraYamagami categories and quantum groups. We show that a
nongrouptheoretical integral modular category of dimension $4q^2$ is
equivalent to either one of these wellknown examples or is of dimension
$36$ and is twistequivalent to fusion categories arising from a
certain quantum group.
Keywords:modular categories, fusion categories Category:18D10 

79. CMB 2014 (vol 57 pp. 431)
 Tagami, Keiji

The Rasmussen Invariant, Fourgenus and Threegenus of an Almost Positive Knot Are Equal
An oriented link is positive if it has a link diagram whose crossings are all positive.
An oriented link is almost positive if it is not positive and has a link diagram with exactly one negative crossing.
It is known that the Rasmussen invariant, $4$genus and $3$genus of a positive knot are equal.
In this paper, we prove that the Rasmussen invariant, $4$genus and $3$genus of an almost positive knot are equal.
Moreover, we determine the Rasmussen invariant of an almost positive knot in terms of its almost positive knot diagram.
As corollaries, we prove that all almost positive knots are not homogeneous, and there is no almost positive knot of $4$genus one.
Keywords:almost positive knot, fourgenus, Rasmussen invariant Categories:57M27, 57M25 

80. CMB 2014 (vol 57 pp. 264)
 Dai, Li; Dong, Jingcheng

On Semisimple Hopf Algebras of Dimension $pq^n$
Let $p,q$ be prime numbers with $p^2\lt q$, $n\in \mathbb{N}$, and $H$ a
semisimple Hopf algebra of dimension $pq^n$ over an algebraically
closed field of characteristic $0$. This paper proves that $H$ must
possess one of the following structures: (1) $H$ is semisolvable;
(2) $H$ is a Radford biproduct $R\# kG$, where $kG$ is the group
algebra of group $G$ of order $p$, and $R$ is a semisimple YetterDrinfeld
Hopf algebra in ${}^{kG}_{kG}\mathcal{YD}$ of dimension $q^n$.
Keywords:semisimple Hopf algebra, semisolvability, Radford biproduct, Drinfeld double Category:16W30 

81. CMB 2014 (vol 57 pp. 765)
 da Silva, Rosângela Maria; Tenenblat, Keti

Helicoidal Minimal Surfaces in a Finsler Space of Randers Type
We consider the Finsler space $(\bar{M}^3, \bar{F})$ obtained by
perturbing the Euclidean metric of $\mathbb{R}^3$ by a rotation. It
is the open region of $\mathbb{R}^3$ bounded by a cylinder with a
Randers metric. Using the BusemannHausdorff volume form, we
obtain the differential equation that characterizes the helicoidal
minimal surfaces in $\bar{M}^3$. We prove that the helicoid is a
minimal surface in $\bar{M}^3$, only if the axis of the helicoid
is the axis of the cylinder. Moreover, we prove that, in the
Randers space $(\bar{M}^3, \bar{F})$, the only minimal
surfaces in the Bonnet family, with fixed axis $O\bar{x}^3$, are the catenoids
and the helicoids.
Keywords:minimal surfaces, helicoidal surfaces, Finsler space, Randers space Categories:53A10, 53B40 

82. CMB 2014 (vol 57 pp. 231)
 Bagherian, J.

On the Multiplicities of Characters in Table Algebras
In this paper we show that every module of a table algebra
can be considered as a faithful module of some quotient table
algebra.
Also we prove that every faithful module of a table algebra
determines a closed subset which is a cyclic group.
As a main result we give some information about multiplicities
of characters in table algebras.
Keywords:table algebra, faithful module, multiplicity of character Categories:20C99, 16G30 

83. CMB 2013 (vol 57 pp. 870)
 Parlier, Hugo

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 

84. CMB 2013 (vol 57 pp. 845)
 Lei, Antonio

Factorisation of Twovariable $p$adic $L$functions
Let $f$ be a modular form which is nonordinary at $p$. Loeffler has
recently constructed four twovariable $p$adic $L$functions
associated to $f$. In the case where $a_p=0$, he showed that, as in
the onevariable 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, padic Lfunctions, supersingular primes Categories:11S40, 11S80 

85. CMB 2013 (vol 57 pp. 463)
 Bownik, Marcin; Jasper, John

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 SchurHorn theorem, the Pythagorean theorem, the Carpenter theorem, spectral theory Categories:42C15, 47B15, 46C05 

86. CMB 2013 (vol 57 pp. 585)
 Lehec, Joseph

Short Probabilistic Proof of the BrascampLieb and Barthe Theorems
We give a short proof of the BrascampLieb 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©kopaLeindler inequality and applies also to the
reversed BrascampLieb inequality, due to Barthe.
Keywords:functional inequalities, Brownian motion Categories:39B62, 60J65 

87. CMB 2013 (vol 57 pp. 526)
 Heil, Wolfgang; Wang, Dongxu

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:LusternikSchnirelmann category, coverings of $3$manifolds by open $K$contractible sets Categories:57N10, 55M30, 57M27, 57N16 

88. CMB 2013 (vol 57 pp. 119)
89. CMB Online first


Leftorderable 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 twobridge knot corresponding to the rational number $3/7$, has leftorderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:leftordering, Dehn surgery Categories:57M25, 06F15 

90. CMB Online first


Leftorderable 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 twobridge knot corresponding to the rational number $3/7$, has leftorderable
fundamental group if the slope $r$ satisfies $0\le r \le 4$.
Keywords:leftordering, Dehn surgery Categories:57M25, 06F15 

91. CMB 2013 (vol 57 pp. 381)
 Łydka, Adrian

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 halfplane 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:Lfunction, MÃ¶bius function, explicit formulae, elliptic curve Categories:11M36, 11G40 

92. CMB 2013 (vol 57 pp. 439)
 Yang, YanHong

The Fixed Point Locus of the Verschiebung on $\mathcal{M}_X(2, 0)$ for Genus2 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 

93. CMB 2013 (vol 57 pp. 245)
 Brodskiy, N.; Dydak, J.; Lang, U.

AssouadNagata 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 AssouadNagata 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:AssouadNagata dimension, asymptotic dimension, wreath product, growth of groups Categories:54F45, 55M10, 54C65 

94. CMB 2013 (vol 57 pp. 310)
95. CMB 2013 (vol 57 pp. 401)
 Perrone, Domenico

Curvature of $K$contact SemiRiemannian Manifolds
In this paper we characterize $K$contact semiRiemannian manifolds
and Sasakian semiRiemannian manifolds in terms of
curvature. Moreover, we show that any conformally flat $K$contact
semiRiemannian 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 semiRiemannian structures, $K$contact structures, conformally flat manifolds, Einstein LorentzianSasaki manifolds Categories:53C50, 53C25, 53B30 

96. CMB 2013 (vol 57 pp. 506)
 Galindo, César

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 

97. CMB 2013 (vol 57 pp. 821)
 Jeong, Imsoon; Kim, Seonhui; Suh, Young Jin

Real Hypersurfaces in Complex TwoPlane Grassmannians with Reeb Parallel Structure Jacobi Operator
In this paper we give a characterization of a real hypersurface of
Type~$(A)$ in complex twoplane 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 twoplane Grassmannians, Hopf hypersurface, Reeb parallel, structure Jacobi operator Categories:53C40, 53C15 

98. CMB 2013 (vol 57 pp. 449)
 Alaghmandan, Mahmood; Choi, Yemon; Samei, Ebrahim

ZLamenability 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 

99. CMB 2013 (vol 57 pp. 254)
 Christensen, Ole; Kim, Hong Oh; Kim, Rae Young

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 UEPtype wavelet systems that
can be extended to a Parseval wavelet frame by adding just one UEPtype wavelet
system. We derive a condition that is necessary for the extension of a UEPtype
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 

100. CMB 2013 (vol 57 pp. 141)
 Mukwembi, Simon

Size, Order, and Connected Domination
We give a sharp upper bound on the size of a
trianglefree 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
trianglefree graphs and answer a question of Griggs, Kleitman and
Shastri on a lower bound of the leaf number in
trianglefree graphs.
Keywords:size, connected domination, local independence number, leaf number Category:05C69 
