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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| Summary: | 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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