Fundamental groups of aspherical manifolds that collapse

Sergio Zamora

Fundamental groups of aspherical manifolds that collapse

Differential Geometry 2021-09-15 v3 Metric Geometry

Authors: Sergio Zamora

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.

Keywords

aspherical manifolds fundamental groups collapse ricci curvature hyperbolic groups riemannian manifolds

Cite

@article{arxiv.2101.06267,
  title  = {Fundamental groups of aspherical manifolds that collapse},
  author = {Sergio Zamora},
  journal= {arXiv preprint arXiv:2101.06267},
  year   = {2021}
}

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