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arXiv · 2506.03377

The McCullough-Miller complex for right angled Artin groups

Peio Ardaiz Galé·Conchita Martínez Pérez
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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 $\ell^2$-Betti numbers or BNRS-invariants. We generalize this construction to pure symmetric automorphism groups of arbitrary RAAGs and exhibit applications of this generalization.

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Peio Ardaiz Galé, Conchita Martínez Pérez. 2025-06-03. The McCullough-Miller complex for right angled Artin groups. https://arxiv.org/abs/2506.03377

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