Higher topological complexity of hyperbolic groups

Journal article

Abstract:: We prove for non-elementary torsion-free hyperbolic groups Γ and all r ≥ 2 that the higher topological complexity TCr(Γ) is equal to r · cd(Γ). In particular, hyperbolic groups satisfy the rationality conjecture on the TC-generating function, giving an affirmative answer to a question of Farber and Oprea. More generally, we show that the same conclusions hold for certain toral relatively hyperbolic groups.

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Publisher:: Springer
Journal:: Journal of Applied and Computational Topology More from this journal
Volume:: 6
Pages:: 323–329
Publication date:: 2022-02-04
Acceptance date:: 2021-12-30
DOI:: 10.1007/s41468-022-00088-4
EISSN:: 2367-1734
ISSN:: 2367-1726

Copyright holder:: Hughes and Li
Rights statement:: © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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