Edge Inversions in $(P_k)$-closed Groups

Kirwin Hampshire; Florian Lehner; Andrew Wood

doi:10.48550/arxiv.2601.18982

Edge Inversions in $(P_k)$-closed Groups

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Kirwin Hampshire, Florian Lehner, Andrew Wood

DOI: 10.48550/arxiv.2601.18982

Cited by: 0

Abstract

We construct $(P_2)$-closed groups acting on $T_3$ in which all edge inversions have infinite order. This provides a negative answer to a question posed by Tornier. We also construct a family of $(P_2)$-closed groups for which the smallest order of an edge inversion is an arbitrarily high finite number.

Fields of Study & Subjects

Geometric and Algebraic Topology Advanced Topology and Set Theory Finite Group Theory Research

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 26 January 2026
Document type: Preprint