Centralizers of torsion in 3-manifold groups

2021/11/01 by Hillman, Jonathan A.
#57K30 #57P10 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2111.01284

Abstract

We show that if P is a PD₃-complex and g∈π₁(P) has finite order >1 and infinite centraliser then π₁(P) retracts onto Z/2Z⊕ℤ. If P is an irreducible closed 3-manifold then it follows from the Projective Plane Theorem that P≅RP²×S¹.

Related

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• Addendum: Virtually Free pro-p groups whose Torsion Elements have finite Centralizer
• Generalized torsion and decomposition of 3-manifolds
• Infinite torsion in Griffiths groups
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