Simple spines of homotopy 2-spheres are unique
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911871154520064 |
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| author | Orson, Patrick Powell, Mark |
| author_facet | Orson, Patrick Powell, Mark |
| contents | A locally flatly embedded $2$-sphere in a compact $4$-manifold $X$ is called a spine if the inclusion map is a homotopy equivalence. A spine is called simple if the complement of the $2$-sphere has abelian fundamental group. We prove that if two simple spines represent the same generator of $H_2(X)$ then they are ambiently isotopic. In particular, the theorem applies to simple shake-slicing $2$-spheres in knot traces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_04207 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Simple spines of homotopy 2-spheres are unique Orson, Patrick Powell, Mark Geometric Topology 57K40, 57N70 A locally flatly embedded $2$-sphere in a compact $4$-manifold $X$ is called a spine if the inclusion map is a homotopy equivalence. A spine is called simple if the complement of the $2$-sphere has abelian fundamental group. We prove that if two simple spines represent the same generator of $H_2(X)$ then they are ambiently isotopic. In particular, the theorem applies to simple shake-slicing $2$-spheres in knot traces. |
| title | Simple spines of homotopy 2-spheres are unique |
| topic | Geometric Topology 57K40, 57N70 |
| url | https://arxiv.org/abs/2208.04207 |