Connectivity of partial basis complexes of freely decomposable groups
Geometric Topology
2025-09-26 v2 Group Theory
Abstract
We show that the complex of partial bases of the free group of rank , where vertices are seen up to conjugation, is Cohen--Macaulay of dimension . This positively answers a conjecture raised by Day and Putman. We prove our results in the more general context of freely decomposable groups.
Keywords
Cite
@article{arxiv.2410.17121,
title = {Connectivity of partial basis complexes of freely decomposable groups},
author = {Benjamin Brück and Kevin Ivan Piterman},
journal= {arXiv preprint arXiv:2410.17121},
year = {2025}
}
Comments
12 pages; v2: accepted version with improved exposition and further background in the introduction; to appear in Bull. Lond. Math. Soc