Year: 2026
Type: preprint
Abstract: Let G be a linear group with Kazhdan property (T) generated by d elements. We show that there are generating sets of size d+2 with arbitrarily small Kazhdan constants. We also prove the same conclusion for every finitely generated group admitting a non-elementary convergence action on a compact metrizable space. This includes non-elementary word-hyperbolic and relatively hyperbolic groups, as well as finitely generated non-elementary subgroups of word-hyperbolic groups.
Source: arXiv (Cornell University)
Authors: Gelander, Tsachik, Lubotzky, Alex, Yao, Jvbin
Institutions: Weizmann Institute of Science, East China Normal University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214975649