Deficiency, relation gap and two-dimensional groups
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 ope...
| المؤلفون الرئيسيون: | , |
|---|---|
| التنسيق: | Journal article |
| اللغة: | English |
| منشور في: |
World Scientific Publishing
2023
|
| الملخص: | 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. |
|---|