English

On Artin groups admitting retractions to parabolic subgroups

Group Theory 2024-08-23 v1

Abstract

We generalize the retractions to standard parabolic subgroups for even Artin groups to FC-type Artin groups and other more general families. We prove that these retractions uniquely extend to any parabolic subgroup. We use retractions to generalize the results of Antol\'in and Foniqi that reduce the problem of intersection of parabolic subgroups to weaker conditions. As a corollary, we characterize coherence for the FC case.

Cite

@article{arxiv.2408.12291,
  title  = {On Artin groups admitting retractions to parabolic subgroups},
  author = {Bruno Aaron Cisneros de la Cruz and María Cumplido and Islam Foniqi},
  journal= {arXiv preprint arXiv:2408.12291},
  year   = {2024}
}

Comments

21 pages. Comments are welcome

R2 v1 2026-06-28T18:20:39.149Z