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2021 Median Sets of Isometries in CAT(0) Cube Complexes and Some Applications
Anthony Genevois
Michigan Math. J. Advance Publication 1-46 (2021). DOI: 10.1307/mmj/20195823

Abstract

In this paper, we associate with isometries of CAT(0) cube complexes specific subspaces, referred to as median sets, which play a similar role as minimizing sets of semisimple isometries in CAT(0) spaces. Various applications are deduced, including a cubulation of centralizers, a splitting theorem, a proof that Dehn twists in mapping class groups must be elliptic for every action on a CAT(0) cube complex, a cubical version of the flat torus theorem, and a structural theorem about polycyclic groups acting on CAT(0) cube complexes.

Citation

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Anthony Genevois. "Median Sets of Isometries in CAT(0) Cube Complexes and Some Applications." Michigan Math. J. Advance Publication 1 - 46, 2021. https://doi.org/10.1307/mmj/20195823

Information

Received: 28 October 2019; Revised: 2 December 2020; Published: 2021
First available in Project Euclid: 12 May 2021

Digital Object Identifier: 10.1307/mmj/20195823

Subjects:
Primary: 20F65
Secondary: 20F16 , 20F67

Rights: Copyright © 2021 The University of Michigan

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