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Hyperbolic isometries and boundaries of systolic complexes

Prytuła, T. (2019). Hyperbolic isometries and boundaries of systolic complexes. Journal of the London Mathematical Society, 99(2), 583-608. doi:10.1112/jlms.12184.

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Genre: Journal Article

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arXiv:1705.01062.pdf (Preprint), 349KB
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Prytula_Hyperbolic isometries and boundaries of systolic complexes_2019.pdf (Publisher version), 536KB

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https://doi.org/10.1112/jlms.12184 (Publisher version)
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Creators:
Prytuła, Tomasz1, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201

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Free keywords: Mathematics, Group Theory
Abstract: Given a group $G$ acting geometrically on a systolic complex $X$ and a hyperbolic isometry $h \in G$, we study the associated action of $h$ on the systolic boundary $\partial X$. We show that $h$ has a canonical pair of fixed points on the boundary and that it acts trivially on the boundary if and only if it is virtually central. The key tool that we use to study the action of $h$ on $\partial X$ is the notion of a $K$-displacement set of $h$, which generalises the classical minimal displacement set of $h$. We also prove that systolic complexes equipped with a geometric action of a group are almost extendable.

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Language(s): eng - English
Dates: 2019
Publication Status: Published in print
Pages: 26
Publishing info: -
Rev. Method: Peer
Identifiers: arXiv: 1705.01062
DOI: 10.1112/jlms.12184
URI: http://arxiv.org/abs/1705.01062
Degree: -

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Title: Journal of the London Mathematical Society
Abbreviation : J. Lond. Math. Soc.
Source Genre: Journal
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Publ. Info: Wiley
Pages: - Volume / Issue: 99 (2) Sequence Number: - Start / End Page: 583 - 608 Identifier: -