Self-covering, finiteness, commutativity, and fibering over tori
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917047789682688 |
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| author | Qin, Lizhen Su, Yang |
| author_facet | Qin, Lizhen Su, Yang |
| contents | A topological space is called self-covering if it is a nontrivial cover of itself. We prove that, under mild assumptions, a closed self-covering manifold with an abelian fundamental group fibers over a torus in various senses. As a corollary, if its dimension is above $5$ and its fundamental group is free abelian, then it is a fiber bundle over a circle. We also construct non-fibering examples when these assumptions are not fulfilled. In particular, one class of examples illustrates that the structure of self-covering manifolds is more complicated when the fundamental groups are nonabelian, and the corresponding fibering problem encounters significant difficulties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24032 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-covering, finiteness, commutativity, and fibering over tori Qin, Lizhen Su, Yang Geometric Topology Algebraic Geometry Algebraic Topology 57R19, 57R65, 55R10 A topological space is called self-covering if it is a nontrivial cover of itself. We prove that, under mild assumptions, a closed self-covering manifold with an abelian fundamental group fibers over a torus in various senses. As a corollary, if its dimension is above $5$ and its fundamental group is free abelian, then it is a fiber bundle over a circle. We also construct non-fibering examples when these assumptions are not fulfilled. In particular, one class of examples illustrates that the structure of self-covering manifolds is more complicated when the fundamental groups are nonabelian, and the corresponding fibering problem encounters significant difficulties. |
| title | Self-covering, finiteness, commutativity, and fibering over tori |
| topic | Geometric Topology Algebraic Geometry Algebraic Topology 57R19, 57R65, 55R10 |
| url | https://arxiv.org/abs/2510.24032 |