Trees, homology, and automorphism groups of RAAGs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2017
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| _version_ | 1866929303851106304 |
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| author | Aramayona, Javier Fernández, José L. Fernández, Pablo Martínez-Pérez, Conchita |
| author_facet | Aramayona, Javier Fernández, José L. Fernández, Pablo Martínez-Pérez, Conchita |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1707_02481 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Trees, homology, and automorphism groups of RAAGs Aramayona, Javier Fernández, José L. Fernández, Pablo Martínez-Pérez, Conchita Group Theory Combinatorics Probability 20F65 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. |
| title | Trees, homology, and automorphism groups of RAAGs |
| topic | Group Theory Combinatorics Probability 20F65 |
| url | https://arxiv.org/abs/1707.02481 |