The McCullough-Miller complex for right angled Artin groups
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912422091030528 |
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| author | Galé, Peio Ardaiz Pérez, Conchita Martínez |
| author_facet | Galé, Peio Ardaiz Pérez, Conchita Martínez |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_03377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The McCullough-Miller complex for right angled Artin groups Galé, Peio Ardaiz Pérez, Conchita Martínez Group Theory Primary 20J06, 20F36, Secondary 57M07, 55P20 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. |
| title | The McCullough-Miller complex for right angled Artin groups |
| topic | Group Theory Primary 20J06, 20F36, Secondary 57M07, 55P20 |
| url | https://arxiv.org/abs/2506.03377 |