English

The Cohen--Lyndon property in non-metric small-cancellation

Group Theory 2025-10-24 v3 Geometric Topology

Abstract

We show that the Cohen--Lyndon property holds for all non-metric small-cancellation quotients. This generalises the analogous result from the metric small-cancellation setting, and answers a question asked by Lyndon in 1966 and by Wall in his 1979 problem list.

Keywords

Cite

@article{arxiv.2310.20288,
  title  = {The Cohen--Lyndon property in non-metric small-cancellation},
  author = {Macarena Arenas and Karol Duda},
  journal= {arXiv preprint arXiv:2310.20288},
  year   = {2025}
}

Comments

27 pages, 7 figures. Primary article by Arenas handles the C(6) case. Appendix, written jointly with Duda, extends the result to the C(4)-T(4) and C(3)-T(6) settings. Final version accepted for publication