Homological Dehn functions of groups of type FP₂

2020/12/01 by Noel Brady, Brady, Noel, Robert Kropholler +3 · 1 citation
Mathematics · #20F05 #20F65 #20J05 #57M07 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.2012.00730

openalex publication_date 2020/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove foundational results for homological Dehn functions of groups of type FP₂ such as superadditivity and the invariance under quasi-isometry. We then study the homological Dehn functions of Leary's groups G_L(S) providing methods to obtain uncountably many groups with a given homological Dehn function. This allows us to show that there exist groups of type FP₂ with quartic homological Dehn function and unsolvable word problem.

Citations

• Normal and Integral Currents
• �ber unendliche diskontinuierliche Gruppen

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