Embedded surfaces with infinite cyclic knot group
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866918477452804096 |
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| author | Conway, Anthony Powell, Mark |
| author_facet | Conway, Anthony Powell, Mark |
| contents | We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$, to be related by an ambient homeomorphism, and further criteria that imply they are ambiently isotopic. Along the way, we prove that certain pairs of topological $4$-manifolds with infinite cyclic fundamental group, homeomorphic boundaries, and equivalent equivariant intersection forms, are homeomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_13461 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Embedded surfaces with infinite cyclic knot group Conway, Anthony Powell, Mark Geometric Topology 57K40, 57K10, 57N35, We study locally flat, compact, oriented surfaces in $4$-manifolds whose exteriors have infinite cyclic fundamental group. We give algebraic topological criteria for two such surfaces, with the same genus $g$, to be related by an ambient homeomorphism, and further criteria that imply they are ambiently isotopic. Along the way, we prove that certain pairs of topological $4$-manifolds with infinite cyclic fundamental group, homeomorphic boundaries, and equivalent equivariant intersection forms, are homeomorphic. |
| title | Embedded surfaces with infinite cyclic knot group |
| topic | Geometric Topology 57K40, 57K10, 57N35, |
| url | https://arxiv.org/abs/2009.13461 |