Higher topological complexity of hyperbolic groups
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...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Springer
2022
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| _version_ | 1797107918061961216 |
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| author | Hughes, S Li, K |
| author_facet | Hughes, S Li, K |
| author_sort | Hughes, S |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T07:20:54Z |
| format | Journal article |
| id | oxford-uuid:1cf3ffed-2721-4510-9eb1-7a7f968feacb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:20:54Z |
| publishDate | 2022 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:1cf3ffed-2721-4510-9eb1-7a7f968feacb2022-10-19T08:56:27ZHigher topological complexity of hyperbolic groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1cf3ffed-2721-4510-9eb1-7a7f968feacbEnglishSymplectic ElementsSpringer2022Hughes, SLi, KWe 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. |
| spellingShingle | Hughes, S Li, K Higher topological complexity of hyperbolic groups |
| title | Higher topological complexity of hyperbolic groups |
| title_full | Higher topological complexity of hyperbolic groups |
| title_fullStr | Higher topological complexity of hyperbolic groups |
| title_full_unstemmed | Higher topological complexity of hyperbolic groups |
| title_short | Higher topological complexity of hyperbolic groups |
| title_sort | higher topological complexity of hyperbolic groups |
| work_keys_str_mv | AT hughess highertopologicalcomplexityofhyperbolicgroups AT lik highertopologicalcomplexityofhyperbolicgroups |