Trees, homology, and automorphism groups of right-angled Artin groups
We study the homology of an explicit finite-index subgroupof the automorphism group of a partially commutative group, in thecase when its defining graph is a tree. More concretely, we give a lowerbound on the first Betti number of this subgroup, based on the numberand degree of a certain type of ver...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Estado: | Versión enviada para evaluación y publicación |
| Data de publicação: | 2018 |
| País: | España |
| Recursos: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repositório: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/228937 |
| Acesso em linha: | http://hdl.handle.net/10261/228937 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Automorphism groups RAAGs Trees Betti numbers Lowerbounds Symbolic method Exponential generating functions |
| Resumo: | We study the homology of an explicit finite-index subgroupof the automorphism group of a partially commutative group, in thecase when its defining graph is a tree. More concretely, we give a lowerbound on the first Betti number of this subgroup, based on the numberand degree of a certain type of vertices, which we calldeep. We thenuse combinatorial methods to analyze the average value of this Bettinumber, in terms of the size of the defining tree. |
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