Stable homology of Higman--Thompson groups via scanning methods
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915758361018368 |
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| author | Delarue, Marie-Camille |
| author_facet | Delarue, Marie-Camille |
| contents | The Higman--Thompson groups $V_{n,r}$ consist of piecewise linear automorphisms of $r$ intervals where cut points and slopes are $n$-adic.
Szymik and Wahl prove homological stability for this family of groups as $r$ increases, and compute the stable homology to be that of the infinite loop space of the Moore spectrum.
We give a new proof of this result using scanning methods on a topological model for the disjoint union of these groups.
We use Thumann's framework of operad groups to build this model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable homology of Higman--Thompson groups via scanning methods Delarue, Marie-Camille Algebraic Topology The Higman--Thompson groups $V_{n,r}$ consist of piecewise linear automorphisms of $r$ intervals where cut points and slopes are $n$-adic. Szymik and Wahl prove homological stability for this family of groups as $r$ increases, and compute the stable homology to be that of the infinite loop space of the Moore spectrum. We give a new proof of this result using scanning methods on a topological model for the disjoint union of these groups. We use Thumann's framework of operad groups to build this model. |
| title | Stable homology of Higman--Thompson groups via scanning methods |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2510.13579 |