Automorphism groups of combinatorial Hantzsche-Wendt groups

Rafał Lutowski; Andrzej Szczepański; Richard Weidmann

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arXiv · 2401.05141

Automorphism groups of combinatorial Hantzsche-Wendt groups

Rafał Lutowski·Andrzej Szczepański·Richard Weidmann

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Abstract

Combinatorial Hantzsche-Wendt groups were introduced by W. Craig and P.A. Linnell. Every such a group $G_n$, where $n$ is a natural number, encodes the holonomy action of any $n+1$-dimensional Hantzsche-Wendt manifold. $G_2$ is the fundamental group of the classical Hantzsche-Wendt manifold -- the only one $3$-dimensional oriented flat manifold with non-cyclic holonomy group. In this article, we describe the structure of the automorphism and of the outer automorphism groups of combinatorial Hantzsche-Wendt groups.

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Rafał Lutowski, Andrzej Szczepański, Richard Weidmann. 2024-01-10. Automorphism groups of combinatorial Hantzsche-Wendt groups. https://arxiv.org/abs/2401.05141

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