Asymptotically rigid mapping class groups of infinite graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915470081261568 |
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| author | Hill, Thomas Kwak, Sanghoon Udall, Brian West, Jeremy |
| author_facet | Hill, Thomas Kwak, Sanghoon Udall, Brian West, Jeremy |
| contents | We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the graph has finitely many ends, we construct an explicit presentation for the so-called pure graph Houghton group and investigate several of its algebraic and geometric properties. Additionally, we show that the graph Houghton groups are not commensurable with other known Houghton-type groups, namely the classical, surface, braided, handlebody, and doubled handlebody Houghton groups, demonstrating that this graph-based construction defines a genuinely new class of groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21264 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotically rigid mapping class groups of infinite graphs Hill, Thomas Kwak, Sanghoon Udall, Brian West, Jeremy Geometric Topology Group Theory 20F65, 57M60, 20F05, 57S05 We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the graph has finitely many ends, we construct an explicit presentation for the so-called pure graph Houghton group and investigate several of its algebraic and geometric properties. Additionally, we show that the graph Houghton groups are not commensurable with other known Houghton-type groups, namely the classical, surface, braided, handlebody, and doubled handlebody Houghton groups, demonstrating that this graph-based construction defines a genuinely new class of groups. |
| title | Asymptotically rigid mapping class groups of infinite graphs |
| topic | Geometric Topology Group Theory 20F65, 57M60, 20F05, 57S05 |
| url | https://arxiv.org/abs/2508.21264 |