Torsion homology growth and cheap rebuilding of inner-amenable groups
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929529639927808 |
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| author | Uschold, Matthias |
| author_facet | Uschold, Matthias |
| contents | We prove that virtually torsion-free, residually finite groups that are inner-amenable and non-amenable have the cheap 1-rebuilding property, a notion recently introduced by Abért, Bergeron, Frączyk and Gaboriau. As a consequence, the first $\ell^2$-Betti number with arbitrary field coefficients and log-torsion in degree 1 vanish for these groups. This extends results previously known for amenable groups to inner-amenable groups. We use a structure theorem of Tucker-Drob for inner-amenable groups showing the existence of a chain of q-normal subgroups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07916 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Torsion homology growth and cheap rebuilding of inner-amenable groups Uschold, Matthias Group Theory Algebraic Topology Geometric Topology 57M07, 20E26, 43A07 We prove that virtually torsion-free, residually finite groups that are inner-amenable and non-amenable have the cheap 1-rebuilding property, a notion recently introduced by Abért, Bergeron, Frączyk and Gaboriau. As a consequence, the first $\ell^2$-Betti number with arbitrary field coefficients and log-torsion in degree 1 vanish for these groups. This extends results previously known for amenable groups to inner-amenable groups. We use a structure theorem of Tucker-Drob for inner-amenable groups showing the existence of a chain of q-normal subgroups. |
| title | Torsion homology growth and cheap rebuilding of inner-amenable groups |
| topic | Group Theory Algebraic Topology Geometric Topology 57M07, 20E26, 43A07 |
| url | https://arxiv.org/abs/2212.07916 |