Asymptotically rigid mapping class groups I: Finiteness properties of braided Thompson's and Houghton's groups
| Autor: | Genevois, Anthony, Lonjou, Anne, Urech, Christian |
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| Rok vydání: | 2020 |
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| Zdroj: | Geom. Topol. 26 (2022) 1385-1434 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/gt.2022.26.1385 |
| Popis: | This article is dedicated to the study of asymptotically rigid mapping class groups of infinitely-punctured surfaces obtained by thickening planar trees. Such groups include the braided Ptolemy-Thompson groups $T^\sharp,T^\ast$ introduced by Funar and Kapoudjian, and the braided Houghton groups $\mathrm{br}H_n$ introduced by Degenhardt. We present an elementary construction of a contractible cube complex, on which these groups act with cube-stabilisers isomorphic to finite extensions of braid groups. As an application, we prove Funar-Kapoudjian's and Degenhardt's conjectures by showing that $T^\sharp,T^\ast$ are of type $F_\infty$ and that $\mathrm{br}H_n$ is of type $F_{n-1}$ but not of type $F_n$. Comment: 36 pages, 11 figures. Comments are welcome! |
| Databáze: | arXiv |
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