Year: 2022
Type: article
Abstract: We prove for non-elementary torsion-free hyperbolic groups $$\Gamma $$ Γ and all $$r\ge 2$$ r ≥ 2 that the higher topological complexity $${\textsf {TC}}_r(\Gamma )$$ TC r ( Γ ) is equal to $$r\cdot \mathrm {cd}(\Gamma )$$ r · cd ( Γ ) . In particular, hyperbolic groups satisfy the rationality conjecture on the $${\textsf {TC}}$$ 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.
Authors: Sam Hughes, Kevin Li
Institutions: University of Oxford, University of Southampton
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,890
OpenAlex ID: W3205225800