English

The McCullough-Miller complex for right angled Artin groups

Group Theory 2025-06-11 v2

Abstract

McCullough and Miller constructed a contractible complex on which the pure symmetric automorphism group of a free group acts with free abelian stabilizers. This complex has been used for computations such as the cohomological dimension of these groups, their cohomology rings, and results about 2\ell^2-Betti numbers or BNRS-invariants. We generalize this construction to pure symmetric automorphism groups of arbitrary RAAGs and exhibit applications of this generalization.

Cite

@article{arxiv.2506.03377,
  title  = {The McCullough-Miller complex for right angled Artin groups},
  author = {Peio Ardaiz Galé and Conchita Martínez Pérez},
  journal= {arXiv preprint arXiv:2506.03377},
  year   = {2025}
}

Comments

34 pages, 7 figures

R2 v1 2026-07-01T02:57:58.043Z