# Torsion homologique dans les revêtements finis

Abstract : The main subject of this thesis is the study of the homology and cohomology of three--manifolds with integer coefficients, with an emphasis on their torsion subgroups. We are mainly intersted in studying the latter in sequence of finite covers and this last problem is related to that of approximating $\ell^2$ invariants by finite ones. In a first part (corresponding to Chapters 1 and 2) we study abelian covering spaces of CW complexes. We prove in all generality results on the growth of the torsion part of the homology groups in sequences of cyclic covers and partial results for more general abelian covering spaces. The second part (which comprises Chapters 3 through 6 and the Appendix A) deals with finite-volume hyperbolic 3--manifolds. We study the problem of approximation for L2-analytic invariants in general setting before turning to the exclusive study of congruence manifolds. For these we also deal with Reidemeister torsions and integral homologies.
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https://tel.archives-ouvertes.fr/tel-01787222
Contributor : Jean Raimbault <>
Submitted on : Wednesday, May 16, 2018 - 1:26:47 PM
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Jean Raimbault. Torsion homologique dans les revêtements finis. Topologie géométrique [math.GT]. Ecole doctorale Paris centre, 2012. Français. ⟨tel-01787222⟩

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