The Euler Characteristic of Spherical Bestvina-Brady Kernels

@misc{martinez2026euler,
  title = {{The Euler Characteristic of Spherical Bestvina-Brady Kernels}},
  author = {Eduardo Flores Martínez},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19203},
  eprint = {2610.19203},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19203},
}

TY  - UNPB
TI  - The Euler Characteristic of Spherical Bestvina-Brady Kernels
AU  - Eduardo Flores Martínez
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.19203
UR  - https://arxiv.org/abs/2610.19203
AB  - We compute the Euler characteristic of Bestvina-Brady kernels BB(Γ) for all Artin groups of spherical type. Our method involves discrete Morse theory to describe the cellular structure of a classifying space for the Bestvina--Brady kernel, through the action of BB(Γ) on non-integer level sets of the universal cover of the Salvetti complex. We extend the method of computation of χ(BB(Γ)) to Artin groups that satisfy the K(π,1)-conjecture and whose nerves are rationally acyclic, and we provide an example by realising the projective plane as the nerve of a Coxeter group.
ER  -