Fundamental groups of aspherical manifolds that collapse

Sergio Zamora

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arXiv · 2101.06267

Fundamental groups of aspherical manifolds that collapse

Sergio Zamora

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Abstract

We show that if a sequence $M_n$ of closed aspherical $d$-dimensional Riemannian manifolds with Ricci curvature uniformly bounded below and diameter uniformly bounded above collapses, then for all large enough $n$, the fundamental groups $\pi_1(M_n)$ have non-trivial finitely generated abelian normal subgroups. In particular, the groups $\pi_1(M_n)$ cannot be non-elementary hyperbolic.

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Sergio Zamora. 2021-01-15. Fundamental groups of aspherical manifolds that collapse. https://arxiv.org/abs/2101.06267

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