Centralizers of torsion in 3-manifold groups

Jonathan A. Hillman

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arXiv · 2111.01284

Centralizers of torsion in 3-manifold groups

Jonathan A. Hillman

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Abstract

We show that if $P$ is a $PD_3$-complex and $g\inπ_1(P)$ has finite order $>1$ and infinite centraliser then $π_1(P)$ retracts onto $Z/2Z\oplus\mathbb{Z}$. If $P$ is an irreducible closed 3-manifold then it follows from the Projective Plane Theorem that $P\cong{RP^2}\times{S^1}$.

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Jonathan A. Hillman. 2021-11-17. Centralizers of torsion in 3-manifold groups. https://arxiv.org/abs/2111.01284

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