Small Kazhdan constants for small generating sets of linear groups

@misc{gelander2026small,
  title = {{Small Kazhdan constants for small generating sets of linear groups}},
  author = {Tsachik Gelander and Alex Lubotzky and Jvbin Yao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36098},
  eprint = {2609.36098},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36098},
  note = {CC0},
}

TY  - UNPB
TI  - Small Kazhdan constants for small generating sets of linear groups
AU  - Tsachik Gelander
AU  - Alex Lubotzky
AU  - Jvbin Yao
PY  - 2026
DA  - 2026/09/28
PB  - arXiv
DO  - 10.48550/arxiv.2609.36098
UR  - https://arxiv.org/abs/2609.36098
AB  - 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.
ER  -