Centralizers of torsion in 3-manifold groups

Jonathan A. Hillman

Centralizers of torsion in 3-manifold groups

Geometric Topology 2021-11-19 v2

Authors: Jonathan A. Hillman

Abstract

We show that if $P$ is a $PD_3$ -complex and $g\in\pi_1(P)$ has finite order $>1$ and infinite centraliser then $\pi_1(P)$ retracts onto $Z/2Z\oplus\mathbb{Z}$ . If $P$ is an irreducible closed 3-manifold then it follows from the Projective Plane Theorem that $P\cong{RP^2}\times{S^1}$ .

Keywords

3-manifold groups torsion elements centralizers pd3-complexes irreducible 3-manifolds

Cite

@article{arxiv.2111.01284,
  title  = {Centralizers of torsion in 3-manifold groups},
  author = {Jonathan A. Hillman},
  journal= {arXiv preprint arXiv:2111.01284},
  year   = {2021}
}

Comments

v2: added three questions relating to possible analogues of the Projective Plane Theorem, and a new section giving alternative arguments due (separately) to J.S. Crisp and G.A. Swarup

Centralizers of torsion in 3-manifold groups

Abstract

Keywords

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