Trees, homology, and automorphism groups of RAAGs
Group Theory
2024-04-09 v1 Combinatorics
Probability
Abstract
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.
Keywords
Cite
@article{arxiv.1707.02481,
title = {Trees, homology, and automorphism groups of RAAGs},
author = {Javier Aramayona and José L. Fernández and Pablo Fernández and Conchita Martínez-Pérez},
journal= {arXiv preprint arXiv:1707.02481},
year = {2024}
}