Connectivity of partial basis complexes of freely decomposable groups

2024/10/22 by Benjamin Brück, Brück, Benjamin, Kevin Iván Piterman +1
Chemistry · Mathematics · #20E06 #20F65 #57M07 #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Graph theory and applications #Group Theory (math.GR) #Organometallic Complex Synthesis and Catalysis

paper · pdf · doi:10.48550/arxiv.2410.17121

openalex publication_date 2024/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the complex of partial bases of the free group of rank n, where vertices are seen up to conjugation, is Cohen--Macaulay of dimension n-1. This positively answers a conjecture raised by Day and Putman. We prove our results in the more general context of freely decomposable groups.

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