On Torelli groups and Dehn twists of smooth 4-manifolds
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866915071704170496 |
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| author | Krannich, Manuel Kupers, Alexander |
| author_facet | Krannich, Manuel Kupers, Alexander |
| contents | This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of $S^4$. Secondly, we give an alternative proof of a consequence of work of Saeki, namely that the Dehn twist along the boundary sphere of a simply-connected closed smooth $4$-manifold $X$ with $\partial X\cong S^3$ is trivial after taking connected sums with enough copies of $S^2\times S^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_08904 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On Torelli groups and Dehn twists of smooth 4-manifolds Krannich, Manuel Kupers, Alexander Geometric Topology Algebraic Topology 57K40, 57S05 This note has two related but independent parts. Firstly, we prove a generalisation of a recent result of Gay on the smooth mapping class group of $S^4$. Secondly, we give an alternative proof of a consequence of work of Saeki, namely that the Dehn twist along the boundary sphere of a simply-connected closed smooth $4$-manifold $X$ with $\partial X\cong S^3$ is trivial after taking connected sums with enough copies of $S^2\times S^2$. |
| title | On Torelli groups and Dehn twists of smooth 4-manifolds |
| topic | Geometric Topology Algebraic Topology 57K40, 57S05 |
| url | https://arxiv.org/abs/2105.08904 |