On a volume invariant of 3-manifolds
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917584394256384 |
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| author | Kegel, Marc Ray, Arunima Spreer, Jonathan Thompson, Em Tillmann, Stephan |
| author_facet | Kegel, Marc Ray, Arunima Spreer, Jonathan Thompson, Em Tillmann, Stephan |
| contents | This paper investigates a real-valued topological invariant of 3-manifolds called topological volume. For a given 3-manifold M it is defined as the smallest volume of the complement of a (possibly empty) hyperbolic link in M. Various refinements of this invariant are given, asymptotically tight upper and lower bounds are determined, and all non-hyperbolic closed 3-manifolds with topological volume of at most 3.07 are classified. Moreover, it is shown that for all but finitely many lens spaces, the volume minimiser is obtained by Dehn filling one of the cusps of the complement of the Whitehead link or its sister manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04839 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a volume invariant of 3-manifolds Kegel, Marc Ray, Arunima Spreer, Jonathan Thompson, Em Tillmann, Stephan Geometric Topology 57K10, 57K31, 57K32, 57R65 This paper investigates a real-valued topological invariant of 3-manifolds called topological volume. For a given 3-manifold M it is defined as the smallest volume of the complement of a (possibly empty) hyperbolic link in M. Various refinements of this invariant are given, asymptotically tight upper and lower bounds are determined, and all non-hyperbolic closed 3-manifolds with topological volume of at most 3.07 are classified. Moreover, it is shown that for all but finitely many lens spaces, the volume minimiser is obtained by Dehn filling one of the cusps of the complement of the Whitehead link or its sister manifold. |
| title | On a volume invariant of 3-manifolds |
| topic | Geometric Topology 57K10, 57K31, 57K32, 57R65 |
| url | https://arxiv.org/abs/2402.04839 |