| dc.contributor.author | Kronheimer, P. B. | |
| dc.contributor.author | Mrowka, Tomasz S. | |
| dc.date.accessioned | 2012-04-27T22:04:24Z | |
| dc.date.available | 2012-04-27T22:04:24Z | |
| dc.date.issued | 2011-11 | |
| dc.identifier.issn | 0073-8301 | |
| dc.identifier.issn | 1618-1913 | |
| dc.identifier.uri | http://hdl.handle.net/1721.1/70474 | |
| dc.description.abstract | We prove that a knot is the unknot if and only if its reduced Khovanov cohomology has rank 1. The proof has two steps. We show first that there is a spectral sequence beginning with the reduced Khovanov cohomology and abutting to a knot homology defined using singular instantons. We then show that the latter homology is isomorphic to the instanton Floer homology of the sutured knot complement: an invariant that is already known to detect the unknot. | en_US |
| dc.language.iso | en_US | |
| dc.publisher | Springer-Verlag | en_US |
| dc.relation.isversionof | http://dx.doi.org/10.1007/s10240-010-0030-y | en_US |
| dc.rights | Creative Commons Attribution-Noncommercial-Share Alike 3.0 | en_US |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/3.0/ | en_US |
| dc.source | arXiv | en_US |
| dc.title | Khovanov homology is an unknot-detector | en_US |
| dc.type | Article | en_US |
| dc.identifier.citation | Kronheimer, P. B., and T. S. Mrowka. “Khovanov Homology Is an Unknot-detector.” Publications mathématiques de l’IHÉS 113.1 (2011): 97–208. Web. 27 Apr. 2012. © 2011 IHES and Springer-Verlag | en_US |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
| dc.contributor.approver | Mrowka, Tomasz S. | |
| dc.contributor.mitauthor | Mrowka, Tomasz S. | |
| dc.relation.journal | Publications Mathématiques de L'IHÉS | en_US |
| dc.eprint.version | Author's final manuscript | en_US |
| dc.type.uri | http://purl.org/eprint/type/JournalArticle | en_US |
| eprint.status | http://purl.org/eprint/status/PeerReviewed | en_US |
| dspace.orderedauthors | Kronheimer, P. B.; Mrowka, T. S. | en |
| dc.identifier.orcid | https://orcid.org/0000-0001-9520-6535 | |
| mit.license | OPEN_ACCESS_POLICY | en_US |
| mit.metadata.status | Complete | |
