Integer surgeries rational homology cobordant to lens spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911928380555264 |
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| author | Fung, Antony T. H. |
| author_facet | Fung, Antony T. H. |
| contents | The Cyclic Surgery Theorem and Moser's work on surgeries on torus knots imply that for any non-trivial knot in $S^3$, there are at most two integer surgeries that produce a lens space. This paper investigates how many positive integer surgeries on a given knot in $S^3$ can produce a manifold rational homology cobordant to a lens space. Tools include Greene and McCoy's work on changemaker lattices which come from Heegaard Floer $d$-invariants, and Aceto-Celoria-Park's work on rational cobordisms and integral homology which is based on Lisca's work on lens spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_11736 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integer surgeries rational homology cobordant to lens spaces Fung, Antony T. H. Geometric Topology 57K10, 57N70 The Cyclic Surgery Theorem and Moser's work on surgeries on torus knots imply that for any non-trivial knot in $S^3$, there are at most two integer surgeries that produce a lens space. This paper investigates how many positive integer surgeries on a given knot in $S^3$ can produce a manifold rational homology cobordant to a lens space. Tools include Greene and McCoy's work on changemaker lattices which come from Heegaard Floer $d$-invariants, and Aceto-Celoria-Park's work on rational cobordisms and integral homology which is based on Lisca's work on lens spaces. |
| title | Integer surgeries rational homology cobordant to lens spaces |
| topic | Geometric Topology 57K10, 57N70 |
| url | https://arxiv.org/abs/2405.11736 |