Problems on handlebody groups
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866910037206630400 |
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| author | Andrew, Naomi Hensel, Sebastian Hughes, Sam Wade, Richard D. |
| author_facet | Andrew, Naomi Hensel, Sebastian Hughes, Sam Wade, Richard D. |
| contents | We survey a number of constructions and open problems related to the handlebody group, with a focus on recent trends in geometric group theory, (co)homological properties, and its relationship to outer automorphism groups of free groups. We also briefly describe how the \emph{cheap $α$-rebuilding property} of Abert, Bergeron, Fraczyk, and Gaboriau can be applied using the disc complex to deduce results about the homology growth of the handlebody group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Problems on handlebody groups Andrew, Naomi Hensel, Sebastian Hughes, Sam Wade, Richard D. Group Theory Geometric Topology 20F65 (Primary) 20E18, 20E26, 20E36, 20J05, 20J06, 57K20, 57M07, 57M99 (Secondary) We survey a number of constructions and open problems related to the handlebody group, with a focus on recent trends in geometric group theory, (co)homological properties, and its relationship to outer automorphism groups of free groups. We also briefly describe how the \emph{cheap $α$-rebuilding property} of Abert, Bergeron, Fraczyk, and Gaboriau can be applied using the disc complex to deduce results about the homology growth of the handlebody group. |
| title | Problems on handlebody groups |
| topic | Group Theory Geometric Topology 20F65 (Primary) 20E18, 20E26, 20E36, 20J05, 20J06, 57K20, 57M07, 57M99 (Secondary) |
| url | https://arxiv.org/abs/2502.21177 |