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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.01921 |
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| _version_ | 1866909091256860672 |
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| author | Hughes, Sam Ruberman, Daniel |
| author_facet | Hughes, Sam Ruberman, Daniel |
| contents | For each integer $n$ we construct a simply connected $4$-manifold $X$ admitting a smoothly embedded surface $Σ$ of self intersection number $n$ such that the complement of the surface has non-trivial fundamental group. This answers a question of Kronheimer in Kirby's 1997 problem list. The proof combines a topological construction with homological properties of simple groups such as Thompson's group $V$ and certain sporadic finite simple groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01921 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Simple groups and complements of smooth surfaces in simply connected $4$-manifolds Hughes, Sam Ruberman, Daniel Geometric Topology 57R40 (primary), 20E32, 20J06 (secondary) For each integer $n$ we construct a simply connected $4$-manifold $X$ admitting a smoothly embedded surface $Σ$ of self intersection number $n$ such that the complement of the surface has non-trivial fundamental group. This answers a question of Kronheimer in Kirby's 1997 problem list. The proof combines a topological construction with homological properties of simple groups such as Thompson's group $V$ and certain sporadic finite simple groups. |
| title | Simple groups and complements of smooth surfaces in simply connected $4$-manifolds |
| topic | Geometric Topology 57R40 (primary), 20E32, 20J06 (secondary) |
| url | https://arxiv.org/abs/2402.01921 |