Knot homology groups from instantons
For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities. In the case of SU(2), the resulting Floer homology group for classical knots appears to be related to Khovanov homology.
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Oxford University Press - London Mathematical Society
2015
|
| Online Access: | http://hdl.handle.net/1721.1/93165 https://orcid.org/0000-0001-9520-6535 |
| _version_ | 1826211511846043648 |
|---|---|
| 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 | For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities. In the case of SU(2), the resulting Floer homology group for classical knots appears to be related to Khovanov homology. |
| first_indexed | 2024-09-23T15:07:09Z |
| format | Article |
| id | mit-1721.1/93165 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:07:09Z |
| publishDate | 2015 |
| publisher | Oxford University Press - London Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/931652022-10-02T00:40:20Z Knot homology groups from instantons Kronheimer, P. B. Mrowka, Tomasz S. Massachusetts Institute of Technology. Department of Mathematics Mrowka, Tomasz S. For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities. In the case of SU(2), the resulting Floer homology group for classical knots appears to be related to Khovanov homology. National Science Foundation (U.S.) (Grant DMS-0206485) National Science Foundation (U.S.) (Grant DMS-0244663) National Science Foundation (U.S.) (Grant DMS-0805841) 2015-01-22T21:49:35Z 2015-01-22T21:49:35Z 2011-12 2010-07 Article http://purl.org/eprint/type/JournalArticle 1753-8416 1753-8424 http://hdl.handle.net/1721.1/93165 Kronheimer, P. B., and T. S. Mrowka. “Knot Homology Groups from Instantons.” Journal of Topology 4, no. 4 (November 29, 2011): 835–918. https://orcid.org/0000-0001-9520-6535 en_US http://dx.doi.org/10.1112/jtopol/jtr024 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. Knot homology groups from instantons |
| title | Knot homology groups from instantons |
| title_full | Knot homology groups from instantons |
| title_fullStr | Knot homology groups from instantons |
| title_full_unstemmed | Knot homology groups from instantons |
| title_short | Knot homology groups from instantons |
| title_sort | knot homology groups from instantons |
| url | http://hdl.handle.net/1721.1/93165 https://orcid.org/0000-0001-9520-6535 |
| work_keys_str_mv | AT kronheimerpb knothomologygroupsfrominstantons AT mrowkatomaszs knothomologygroupsfrominstantons |