Dense Conjugacy Classes and Stability of Locally Finite Graphs
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911361268711424 |
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| author | Klein, Rachmiel |
| author_facet | Klein, Rachmiel |
| contents | Mapping class groups of locally finite graphs are the analogue of those of infinite-type surfaces, and serve as a "big" version of $\text{Out}(F_n)$. In this paper, we investigate which of these mapping class groups have a dense conjugacy class. We obtain a complete classification for self-similar locally finite graphs, and show that a large class of mapping class groups do not have a dense conjugacy class. One of the main tools we develop is flux homomorphisms, which we define for a broad class of locally finite graphs. Along the way, we develop a combinatorial notion for locally finite graphs, and we use it to provide a simple criterion for determining whether a locally finite graph is stable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dense Conjugacy Classes and Stability of Locally Finite Graphs Klein, Rachmiel Geometric Topology Group Theory Mapping class groups of locally finite graphs are the analogue of those of infinite-type surfaces, and serve as a "big" version of $\text{Out}(F_n)$. In this paper, we investigate which of these mapping class groups have a dense conjugacy class. We obtain a complete classification for self-similar locally finite graphs, and show that a large class of mapping class groups do not have a dense conjugacy class. One of the main tools we develop is flux homomorphisms, which we define for a broad class of locally finite graphs. Along the way, we develop a combinatorial notion for locally finite graphs, and we use it to provide a simple criterion for determining whether a locally finite graph is stable. |
| title | Dense Conjugacy Classes and Stability of Locally Finite Graphs |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2512.12033 |