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...
| Main Authors: | , |
|---|---|
| Formato: | Journal article |
| Idioma: | English |
| Publicado: |
World Scientific Publishing
2023
|
| _version_ | 1826313634287976448 |
|---|---|
| author | Kar, A Nikolov, NV |
| author_facet | Kar, A Nikolov, NV |
| author_sort | Kar, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T08:23:52Z |
| format | Journal article |
| id | oxford-uuid:e55ee581-507a-482d-8c4c-aca619f6cfd9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:18:00Z |
| publishDate | 2023 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:e55ee581-507a-482d-8c4c-aca619f6cfd92024-07-24T09:37:33ZDeficiency, relation gap and two-dimensional groupsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:e55ee581-507a-482d-8c4c-aca619f6cfd9EnglishSymplectic ElementsWorld Scientific Publishing2023Kar, ANikolov, NVLet 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. |
| spellingShingle | Kar, A Nikolov, NV Deficiency, relation gap and two-dimensional groups |
| title | Deficiency, relation gap and two-dimensional groups |
| title_full | Deficiency, relation gap and two-dimensional groups |
| title_fullStr | Deficiency, relation gap and two-dimensional groups |
| title_full_unstemmed | Deficiency, relation gap and two-dimensional groups |
| title_short | Deficiency, relation gap and two-dimensional groups |
| title_sort | deficiency relation gap and two dimensional groups |
| work_keys_str_mv | AT kara deficiencyrelationgapandtwodimensionalgroups AT nikolovnv deficiencyrelationgapandtwodimensionalgroups |