Outer space for RAAGs
| Autor: | Corey Bregman, Ruth Charney, Karen Vogtmann |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| ISSN: | 0012-7094 |
| Popis: | For any right-angled Artin group $A_{\Gamma}$ we construct a finite-dimensional space $\mathcal{O}_{\Gamma}$ on which the group $\text{Out}(A_{\Gamma})$ of outer automorphisms of $A_{\Gamma}$ acts with finite point stabilizers. We prove that $\mathcal{O}_{\Gamma}$ is contractible, so that the quotient is a rational classifying space for $\text{Out}(A_{\Gamma})$. The space $\mathcal{O}_{\Gamma}$ blends features of the symmetric space of lattices in $\mathbb{R}^n$ with those of Outer space for the free group $F_n$. Points in $\mathcal{O}_{\Gamma}$ are locally CAT(0) metric spaces that are homeomorphic (but not isometric) to certain locally CAT(0) cube complexes, marked by an isomorphism of their fundamental group with $A_{\Gamma}$. Comment: 61 pages, 17 figures. Modified statement of the main theorem, changed exposition, added a figure |
| Databáze: | OpenAIRE |
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