14 research outputs found

    On lower bounds for cohomology growth in p-adic analytic towers

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    Let p and l be two distinct prime numbers and let G be a group. We study the asymptotic behaviour of the mod-l Betti numbers in p-adic analytic towers of finite index subgroups. If X is a finite l-group of automorphisms of G, our main theorem allows to lift lower bounds for the mod-l cohomology growth in the fixed point group G^X to lower bounds for the growth in G. We give applications to S-arithmetic groups and we also obtain a similar result for cohomology with rational coefficients.Comment: 14 pages, final version, to appear in Math. Z. (The final publication is available at link.springer.com

    ON GEOMETRIC ASPECTS OF DIFFUSE GROUPS

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    International audienceBowditch introduced the notion of diffuse groups as a geometric variation of the unique product property. We elaborate on various examples and non-examples, keeping the geometric point of view from Bowditch's paper. In particular, we discuss fundamental groups of flat and hyperbolic manifolds. Appendix B settles an open question by providing an example of a group which is diffuse but not left-orderable

    Profinite invariants of arithmetic groups

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    International audienceWe prove that the sign of the Euler characteristic of arithmetic groups with the congruence subgroup property is determined by the profinite completion. In contrast, we construct examples showing that this is not true for the Euler characteristic itself and that the sign of the Euler characteristic is not profinite among general residually finite groups of type F. Our methods imply similar results for 2-torsion as well as a strong profiniteness statement for Novikov-Shubin invariants.Nous montrons que le signe de la caractéristique d'Euler d'un groupe arithmétique dont tous les sous-groupes d'indice fini sont de conguence ne dépend que de sa complétion profinie. En revanche cela n'est pas le cas pour la caractéristique d'Euler, et nous donnons aussi des exemples de groupes de type F pour lesquels cela le signe lui-même n'est pas un invariant profini. Notre démonstration repose sur les nombres de Betti L2 et nous donnons aussi des résultats pour d'autres invariants L2
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