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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.12740 |
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| _version_ | 1866912820594999296 |
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| author | Bonn, Laura Sauer, Roman |
| author_facet | Bonn, Laura Sauer, Roman |
| contents | We show how finiteness properties of a group and a subgroup transfer to finiteness properties of the Schlichting completion relative to this subgroup. Further, we provide a criterion when the dense embedding of a discrete group into the Schlichting completion relative to one of its subgroups induces an isomorphism in (continuous) cohomology. As an application, we show that the continuous cohomology of the Neretin group vanishes in all positive degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_12740 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On homological properties of the Schlichting completion Bonn, Laura Sauer, Roman Group Theory We show how finiteness properties of a group and a subgroup transfer to finiteness properties of the Schlichting completion relative to this subgroup. Further, we provide a criterion when the dense embedding of a discrete group into the Schlichting completion relative to one of its subgroups induces an isomorphism in (continuous) cohomology. As an application, we show that the continuous cohomology of the Neretin group vanishes in all positive degrees. |
| title | On homological properties of the Schlichting completion |
| topic | Group Theory |
| url | https://arxiv.org/abs/2406.12740 |