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  Metric systolicity and two-dimensional Artin groups

Huang, J., & Osajda, D. (2019). Metric systolicity and two-dimensional Artin groups. Mathematische Annalen, 374(3-4), 1311-1352. doi:10.1007/s00208-019-01823-6.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0004-68DD-F Version Permalink: https://hdl.handle.net/21.11116/0000-0004-737A-2
Genre: Journal Article

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Huang-Osajda_Metric systolicity and two-dimensional Artin groups_2019.pdf (Publisher version), 1009KB
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© The Author(s) 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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https://doi.org/10.1007/s00208-019-01823-6 (Publisher version)
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 Creators:
Huang, Jingyin1, Author           
Osajda, Damian, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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 Abstract: We introduce the notion of metrically systolic simplicial complexes. We study geometric and large-scale properties of such complexes and of groups acting on them geometrically. We show that all two-dimensional Artin groups act geometrically on metrically systolic complexes. As direct corollaries we obtain new results on two-dimensional Artin groups and all their finitely presented subgroups: we prove that the Conjugacy Problem is solvable, and that the Dehn function is quadratic. We also show several large-scale features of finitely presented subgroups of two-dimensional Artin groups, lying background for further studies concerning their quasi-isometric rigidity.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 42
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1007/s00208-019-01823-6
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Title: Mathematische Annalen
  Abbreviation : Math. Ann.
Source Genre: Journal
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Publ. Info: Springer
Pages: - Volume / Issue: 374 (3-4) Sequence Number: - Start / End Page: 1311 - 1352 Identifier: -