Embeddings of mapping tori for end-periodic graph maps
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911275932450816 |
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| author | Smith, Adam R. |
| author_facet | Smith, Adam R. |
| contents | End-periodic homotopy equivalences of infinite, locally finite graphs serve as dimension-one analogs of the end-periodic automorphisms traditionally defined on infinite-type surfaces. We demonstrate that if $Γ$ is an infinite graph with finitely many ends, and $g \colon Γ\to Γ$ is end-periodic, then its mapping torus $Z_g$ admits a flowline-preserving homotopy equivalence with a finite 2-complex. With additional hypotheses on $g$, this compactified mapping torus subsequently embeds in the mapping torus of a homotopy equivalence on a finite-rank graph via a $π_1$-injective, flow-preserving map. We prove that every mapping class of $Γ$ arising from an end-periodic homotopy equivalence contains a representative whose mapping torus realizes such an embedding. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_14976 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Embeddings of mapping tori for end-periodic graph maps Smith, Adam R. Geometric Topology Dynamical Systems End-periodic homotopy equivalences of infinite, locally finite graphs serve as dimension-one analogs of the end-periodic automorphisms traditionally defined on infinite-type surfaces. We demonstrate that if $Γ$ is an infinite graph with finitely many ends, and $g \colon Γ\to Γ$ is end-periodic, then its mapping torus $Z_g$ admits a flowline-preserving homotopy equivalence with a finite 2-complex. With additional hypotheses on $g$, this compactified mapping torus subsequently embeds in the mapping torus of a homotopy equivalence on a finite-rank graph via a $π_1$-injective, flow-preserving map. We prove that every mapping class of $Γ$ arising from an end-periodic homotopy equivalence contains a representative whose mapping torus realizes such an embedding. |
| title | Embeddings of mapping tori for end-periodic graph maps |
| topic | Geometric Topology Dynamical Systems |
| url | https://arxiv.org/abs/2511.14976 |