Trees, homology, and automorphism groups of right-angled Artin groups
We study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree. More concretely, we give a lower bound on the first Betti number of this subgroup, based on the number and degree of a certain type of...
| Authors: | , , , |
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| Format: | article |
| Status: | Versión aceptada para publicación |
| Publication Date: | 2019 |
| Country: | España |
| Institution: | Universidad de Zaragoza |
| Repository: | Zaguán. Repositorio Digital de la Universidad de Zaragoza |
| OAI Identifier: | oai:zaguan.unizar.es:84320 |
| Online Access: | http://zaguan.unizar.es/record/84320 |
| Access Level: | Open access |
| Summary: | We study the homology of an explicit finite-index subgroup of the automorphism group of a partially commutative group, in the case when its defining graph is a tree. More concretely, we give a lower bound on the first Betti number of this subgroup, based on the number and degree of a certain type of vertices, which we call deep. We then use combinatorial methods to analyze the average value of this Betti number, in terms of the size of the defining tree. |
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