Mathematical Proceedings of the Cambridge Philosophical Society
Publisher: Cambridge Philosophical Society, Cambridge University Press
Description
 Impact factor0.68
 5year impact0.74
 Cited halflife0.00
 Immediacy index0.18
 Eigenfactor0.01
 Article influence1.17
 ISSN14698064
 OCLC260004454
 Material typeInternet resource
 Document typeInternet Resource, Computer File, Journal / Magazine / Newspaper
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 Publisher last reviewed on 07/10/2014
 Classification green
Publications in this journal

Article: Coxeter groups and Kähler groups
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ABSTRACT: We study homomorphisms from Kähler groups to Coxeter groups. As an application, we prove that a cocompact complex hyperbolic lattice (in complex dimension at least 2) does not embed into a Coxeter group or a rightangled Artin group. This is in contrast with the case of real hyperbolic lattices.Mathematical Proceedings of the Cambridge Philosophical Society 11/2013; 155(03).  [Show abstract] [Hide abstract]
ABSTRACT: Let 〈a 1, . . ., am ∣ wn 〉 be a presentation of a group G, where n ≥ 2. We define a system of codimension1 subspaces in the universal cover, and invoke Sageev's construction to produce an action of G on a CAT(0) cube complex. We show that the action is proper and cocompact when n ≥ 4. A fundamental tool is a geometric generalization of Pride's C(2n) smallcancellation result. We prove similar results for staggered groups with torsion.Mathematical Proceedings of the Cambridge Philosophical Society 11/2013; 155(03).  [Show abstract] [Hide abstract]
ABSTRACT: In Frobenius' initial papers on group characters he introduced kcharacters in order to give an algorithm to calculate the irreducible factors of the group determinant. We show how his work leads naturally to the construction of a formal power series for any class function on a group, which terminates if and only if the class function is a character. This is then used to obtain a criterion for a class function to be a character.Mathematical Proceedings of the Cambridge Philosophical Society 11/2013; 155(03).  [Show abstract] [Hide abstract]
ABSTRACT: Let f be a primitive modular form of CM type of weight k and level Γ 0 (N). Let p be an odd prime which does not divide N, and for which f is ordinary. Our aim is to padically interpolate suitably normalized versions of the critical values L(f,ρχ,n), where n=1,2,...,k1, ρ is a fixed selfdual Artin representation of M ∞ , and χ runs over the irreducible Artin representations of the Galois group of the cyclotomic ℤ p extension of ℚ. As an application, if k≥4, we show that there are only finitely many χ such that L(f,ρχ,k/2)=0, generalizing a result of D. Rohrlich [Invent. Math. 75, 409–423 (1984; Zbl 0565.14006)]. Also, we conditionally establish a congruence predicted by noncommutative Iwasawa theory and give numerical evidence for it.Mathematical Proceedings of the Cambridge Philosophical Society 11/2013; 155(03).  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we obtain special value results for Lfunctions associated to classical and paramodular SaitoKurokawa lifts. In particular, we consider standard Lfunctions associated to SaitoKurokawa lifts as well as degree eight Lfunctions obtained by twisting with an automorphic form defined on GL(2). The results are obtained by combining classical and representation theoretic arguments.Mathematical Proceedings of the Cambridge Philosophical Society 09/2013; 155(02).  [Show abstract] [Hide abstract]
ABSTRACT: We construct examples of closed nonHaken hyperbolic 3manifolds with a Heegaard splitting of arbitrarily large distance.Mathematical Proceedings of the Cambridge Philosophical Society 11/2012;  [Show abstract] [Hide abstract]
ABSTRACT: We prove a generalisation of Roth's theorem for arithmetic progressions to dconfigurations, which are sets of the form {n_i+n_j+a}_{1 \leq i \leq j \leq d} where a, n_1,..., n_d are nonnegative integers, using Roth's original density increment strategy and Gowers uniformity norms. Then we use this generalisation to improve a result of Sudakov, Szemer\'edi and Vu about sumfree subsets and prove that any set of n integers contains a sumfree subset of size at least log n (log log log n)^{1/32772  o(1)}.Mathematical Proceedings of the Cambridge Philosophical Society 10/2012;  [Show abstract] [Hide abstract]
ABSTRACT: It is shown that if T is a ternary ring of operators (TRO), X is a nondegenerate subTRO of T and there exists a contractive idempotent surjective map P:T>X, then P has a unique, explicitly described extension to a conditional expectation between the associated linking algebras. A version of the result for W*TROs is also presented and some applications mentioned.Mathematical Proceedings of the Cambridge Philosophical Society 09/2012;  [Show abstract] [Hide abstract]
ABSTRACT: We give a method for obtaining infinitely many framed knots which represent a diffeomorphic 4manifold. We also study a relationship between the $n$shake genus and the 4ball genus of a knot. Furthermore we give a construction of homotopy 4spheres from a slice knot with unknotting number one.Mathematical Proceedings of the Cambridge Philosophical Society 09/2012; 
Article: Heat kernel bounds for complex time and Schrödinger Kernel on hyperbolic spaces and Kleinian groups
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ABSTRACT: We obtain sharp heat Kernel bounds for complex time and bounds for the Schrödinger Kernel on hyperbolic spaces and for a class of Kleinian groups as well.Mathematical Proceedings of the Cambridge Philosophical Society 09/2012;  [Show abstract] [Hide abstract]
ABSTRACT: We study the asymptotics of the higher dimensional Reidemeister torsion for torus knot exteriors, which is related to the results by W. M\"uller and P. MenalFerrer and J. Porti on the asymptotics of the Reidemeister torsion and the hyperbolic volumes for hyperbolic 3manifolds. We show that the sequence of log the higher dimensional Reidemeister torsion of a torus knot exterior with SL(2N,C)representation / (2N)^2 converges to zero when N goes to infinity. We also give a classification for SL(2,C)representations of torus knot groups, which induce acyclic SL(2N,C)representations.Mathematical Proceedings of the Cambridge Philosophical Society 08/2012;  [Show abstract] [Hide abstract]
ABSTRACT: We investigate some connectedness properties of the set of points K(f) where the iterates of an entire function f are bounded. In particular, we describe a class of transcendental entire functions for which an analogue of the BrannerHubbard conjecture holds and show that, for such functions, if K(f) is disconnected then it has uncountably many components. We give examples to show that K(f) can be totally disconnected, and we use quasiconformal surgery to construct a function for which K(f) has a component with empty interior that is not a singleton.Mathematical Proceedings of the Cambridge Philosophical Society 08/2012;  [Show abstract] [Hide abstract]
ABSTRACT: Let $L_1$, $L_2$ $L_3$ be integer linear functions with no fixed prime divisor. We show there are infinitely many $n$ for which the product $L_1(n)L_2(n)L_3(n)$ has at most 7 prime factors, improving a result of Porter. We do this by means of a weighted sieve based upon the DiamondHalberstamRichert multidimensional sieve.Mathematical Proceedings of the Cambridge Philosophical Society 05/2012;  [Show abstract] [Hide abstract]
ABSTRACT: The constancy of the Milnor number has several characterizations which were summarized by Greuel in 1986. This paper presents a study of these characterizations in the case of families of functions with isolated singularities defined on an analytic variety.Mathematical Proceedings of the Cambridge Philosophical Society 03/2012; 
Article: A maximin characterisation of the escape rate of nonexpansive mappings in metrically convex spaces
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ABSTRACT: We establish a maximin characterisation of the linear escape rate of the orbits of a nonexpansive mapping on a complete (hemi)metric space, under a mild form of Busemann's nonpositive curvature condition (we require a distinguished family of geodesics with a common origin to satisfy a convexity inequality). This characterisation, which involves horofunctions, generalises the Collatz–Wielandt characterisation of the spectral radius of a nonnegative matrix. It yields as corollaries a theorem of Kohlberg and Neyman (1981), concerning nonexpansive maps in Banach spaces, a variant of a Denjoy–Wolff type theorem of Karlsson (2001), together with a refinement of a theorem of Gunawardena and Walsh (2003), concerning orderpreserving positively homogeneous selfmaps of symmetric cones. An application to zerosum stochastic games is also given.Mathematical Proceedings of the Cambridge Philosophical Society 02/2012; 152(02):341  363.
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