Gauge theory and Rasmussen's invariant
Using a version of instanton homology, an integer invariant s[superscript ♯](K) is defined for knots K in S[superscript 3]. This invariant is shown to be equal to Rasmussen's s-invariant. While Rasmussen's invariant provides a lower bound for 2 g(Σ) for any surface Σ in B[superscript 4] wi...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Oxford University Press - London Mathematical Society
2015
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| Online Access: | http://hdl.handle.net/1721.1/93159 https://orcid.org/0000-0001-9520-6535 |
| _version_ | 1811074533282545664 |
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| author | Kronheimer, P. B. Mrowka, Tomasz S. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kronheimer, P. B. Mrowka, Tomasz S. |
| author_sort | Kronheimer, P. B. |
| collection | MIT |
| description | Using a version of instanton homology, an integer invariant s[superscript ♯](K) is defined for knots K in S[superscript 3]. This invariant is shown to be equal to Rasmussen's s-invariant. While Rasmussen's invariant provides a lower bound for 2 g(Σ) for any surface Σ in B[superscript 4] with boundary K, it is shown in this paper that s[superscript ♯](K) (and therefore s(K)) similarly bounds the genus of such a surface Σ in any homotopy 4-ball. |
| first_indexed | 2024-09-23T09:51:19Z |
| format | Article |
| id | mit-1721.1/93159 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:51:19Z |
| publishDate | 2015 |
| publisher | Oxford University Press - London Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/931592022-09-30T17:13:52Z Gauge theory and Rasmussen's invariant Kronheimer, P. B. Mrowka, Tomasz S. Massachusetts Institute of Technology. Department of Mathematics Mrowka, Tomasz S. Using a version of instanton homology, an integer invariant s[superscript ♯](K) is defined for knots K in S[superscript 3]. This invariant is shown to be equal to Rasmussen's s-invariant. While Rasmussen's invariant provides a lower bound for 2 g(Σ) for any surface Σ in B[superscript 4] with boundary K, it is shown in this paper that s[superscript ♯](K) (and therefore s(K)) similarly bounds the genus of such a surface Σ in any homotopy 4-ball. National Science Foundation (U.S.) (Grant DMS-0805841) 2015-01-22T21:15:24Z 2015-01-22T21:15:24Z 2013-04 2012-08 Article http://purl.org/eprint/type/JournalArticle 1753-8416 1753-8424 http://hdl.handle.net/1721.1/93159 Kronheimer, P. B., and T. S. Mrowka. “Gauge Theory and Rasmussen’s Invariant.” Journal of Topology 6.3 (April 7, 2013): 659–674. https://orcid.org/0000-0001-9520-6535 en_US http://dx.doi.org/10.1112/jtopol/jtt008 Journal of Topology Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press - London Mathematical Society arXiv |
| spellingShingle | Kronheimer, P. B. Mrowka, Tomasz S. Gauge theory and Rasmussen's invariant |
| title | Gauge theory and Rasmussen's invariant |
| title_full | Gauge theory and Rasmussen's invariant |
| title_fullStr | Gauge theory and Rasmussen's invariant |
| title_full_unstemmed | Gauge theory and Rasmussen's invariant |
| title_short | Gauge theory and Rasmussen's invariant |
| title_sort | gauge theory and rasmussen s invariant |
| url | http://hdl.handle.net/1721.1/93159 https://orcid.org/0000-0001-9520-6535 |
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