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  • Articles  (75)
  • 2010-2014  (75)
  • 2014  (75)
  • Mathematics  (75)
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  • Articles  (75)
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  • 2010-2014  (75)
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  • Mathematics  (75)
  • 1
    Publication Date: 2014-11-20
    Description: We classify countable locally finite-by-abelian groups up to coarse isomorphism. Our classification is derived from a coarse classification of amenable shift-homogeneous metric spaces.
    Print ISSN: 0033-5606
    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 2
    Publication Date: 2014-11-20
    Description: It is shown how to use non-commutative stopping times in order to stop the CCR flow of arbitrary index and also its isometric cocycles, i.e. left operator Markovian cocycles on Boson Fock space. Stopping the CCR flow yields a homomorphism from the semigroup of stopping times, equipped with the convolution product, into the semigroup of unital endomorphisms of the von Neumann algebra of bounded operators on the ambient Fock space. The operators produced by stopping cocycles themselves satisfy a cocycle relation.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 3
    Publication Date: 2014-11-20
    Description: We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp (2 N ), SO (2 N ) and O – (2 N ). These averages are used to predict the asymptotic formulae for moments of derivatives of L -functions which arise in number theory. Each formula gives the leading constant of the asymptotic in terms of determinants of hypergeometric functions. We find a differential recurrence relation between these determinants that allows the rapid computation of the ( k +1)st constant in terms of the k th and ( k –1)st. This recurrence is reminiscent of a Toda lattice equation arising in the theory of -functions associated with Painlevé differential equations.
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    Electronic ISSN: 1464-3847
    Topics: Mathematics
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  • 4
    Publication Date: 2014-11-20
    Description: For a family of G -fields K , we show an effective prime ideal theorem with probability 1. Namely, outside a density zero set, ( x , K )=Li( x )+ O ( x /(log x ) 2 ) for x ≥(log d K ) c for some c depending on G . Using the effective prime ideal theorem, we show that the exponents e K of the ideal class groups of a family of G -fields increase along with d K with probability 1.
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    Electronic ISSN: 1464-3847
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  • 5
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    Oxford University Press
    Publication Date: 2014-11-20
    Description: Using -adic cohomology of tensor inductions of lisse $\bar{\mathbb{Q}}_{\ell}$ -sheaves, we study a class of incomplete character sums.
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    Electronic ISSN: 1464-3847
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  • 6
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    Oxford University Press
    Publication Date: 2014-11-20
    Description: Let M 7 be a smooth manifold equipped with a G 2 -structure , and Y 3 be a closed compact -associative submanifold. McLean [Deformations of calibrated submanifolds, Comm. Anal. Geom. 6 (1998), 705–747] proved that the moduli space M Y , of the -associative deformations of Y has vanishing virtual dimension. In this paper, we perturb into a G 2 -structure in order to ensure the smoothness of M Y , near Y . If Y is allowed to have a boundary moving in a fixed coassociative submanifold X , it was proved in Gayet and Witt [Deformations of associative submanifolds with boundary, Adv. Math. 226 (2011), 2351–2370] that the moduli space M Y , X of the associative deformations of Y with boundary in X has finite virtual dimension. We show here that a generic perturbation of the boundary condition X into X ' gives the smoothness of M Y , X ' . In another direction, we use Bochner's technique to prove a vanishing theorem that forces M Y or M Y , X to be smooth near Y . For every case, some explicit families of examples will be given.
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    Topics: Mathematics
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  • 7
    Publication Date: 2014-11-20
    Description: The main purpose of this article is to give the integral cohomology of classical principal congruence subgroups in SL(2, Z) as well as their analogues in the 3-strand braid group with local coefficients in symmetric powers of the natural symplectic representation. The resulting answers (1) correspond to certain modular forms in characteristic zero and (2) the cohomology of certain spaces in homotopy theory in characteristic p . The torsion is given in terms of the structure of a ‘ p -divided power algebra’. The work is an extension of the work in Callegaro et al. [The cohomology of the braid group B 3 and of S L 2 (Z) with coefficients in a geometric representation, Quart. J. Math . 64 (2013), 847–889] as well as extensions of a classical computation of Shimura to integral coefficients. The results here contrast the local coefficients such as that in Looijenga [Stable cohomology of the mapping class group with symplectic coefficients and of the universal Abel–Jacobi map, J. Algebraic Geom. 5 (1996), 135–150] and Tillmann [The representation of the mapping class group of a surface on its fundamental group in stable homology, Quart. J. Math. 61 (2010), 373–380].
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  • 8
    Publication Date: 2014-11-20
    Description: For every irreducible hyperbolic automorphism of F N (i.e. the analog of a pseudo-Anosov mapping class) it is shown that the algebraic lamination dual to the forward limit tree T + () is obtained as ‘diagonal closure’ of the support of the backward limit current μ – (). This diagonal closure is obtained through a finite procedure analogous to adding diagonal leaves from the complementary components to the stable lamination of a pseudo-Anosov homeomorphism. We also give several new characterizations as well as a structure theorem for the dual lamination of T + (), in terms of Bestvina–Feighn–Handel's ‘stable lamination’ associated to .
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  • 9
    Publication Date: 2014-11-20
    Description: In the present paper, we propose and supply evidence for the following conjecture, aimed at characterizing uniform pro- p groups. Suppose that p ≥3 and let G be a torsion-free pro- p group of finite rank. Then G is uniform if and only if its minimal number of generators is equal to the dimension of G as a p -adic manifold, i.e. d ( G ) = dim( G ). In particular, we prove that the assertion is true whenever G is soluble or p 〉 dim( G ).
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  • 10
    Publication Date: 2014-11-20
    Description: We analyse the subgroup structure of direct products of groups. In particular, we seek to relate the finiteness properties of a subgroup to the way it is embedded in the ambient product. The titular conjecture gives a precise criterion for determining the finiteness properties of a fibre product of groups. Using a variety of approaches to this conjecture, we prove a general result on finite generation of homology groups of fibre products as well as results on the stronger finiteness properties F n and FP n , in certain special cases. As a consequence, we make progress on a conjectured characterization on higher finiteness conditions of a subgroup of a direct product of free or limit groups in terms of an embedding condition.
    Print ISSN: 0033-5606
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    Topics: Mathematics
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