Deficiency, relation gap and two-dimensional groups

Journal article

Let G be a finitely presented, residually finite group and let δ(G) denote the deficiency of G . Assume that every subgroup H of finite index in G satisfies δ(H)−1=|G:H|(δ(G)−1) . We conjecture that G has a two-dimensional finite classifying space K(G,1) . This conjecture is motivated by an open question about the deficiency gradient of groups and their L2 -Betti numbers. In this note, we relate this conjecture to the relation gap problem for group presentations. We verify the pro-p version of the conjecture, as well as its higher dimensional abstract analogs.

Authors: Kar, A; Nikolov, NV

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: World Scientific Publishing
• Journal: Journal of Topology and Analysis
• Volume: 17
• Issue: 1
• Pages: 131-141
• Publication date: 2023-07-24
• Acceptance date: 2022-06-14
• DOI: 10.1142/S1793525323500085
• EISSN: 1793-7167
• ISSN: 1793-5253
• Language: English