Exact Triangles for SO(3) Instanton Homology of Webs
The SO(3) instanton homology recently introduced by the authors associates a finite-dimensional vector space over the field of two elements to every embedded trivalent graph (or "web"). The present paper establishes a skein exact triangle for this instanton homology, as well as a realizati...
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| Format: | Article |
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Oxford University Press (OUP)
2018
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| Online Access: | http://hdl.handle.net/1721.1/116014 https://orcid.org/0000-0001-9520-6535 |
| _version_ | 1811090404481695744 |
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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 | The SO(3) instanton homology recently introduced by the authors associates a finite-dimensional vector space over the field of two elements to every embedded trivalent graph (or "web"). The present paper establishes a skein exact triangle for this instanton homology, as well as a realization of the octahedral axiom. From the octahedral diagram, one can derive equivalent reformulations of the authors' conjecture that, for planar webs, the rank of the instanton homology is equal to the number of Tait colorings. |
| first_indexed | 2024-09-23T14:44:44Z |
| format | Article |
| id | mit-1721.1/116014 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T14:44:44Z |
| publishDate | 2018 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1160142022-10-01T22:15:38Z Exact Triangles for SO(3) Instanton Homology of Webs Kronheimer, P. B. Mrowka, Tomasz S Massachusetts Institute of Technology. Department of Mathematics Mrowka, Tomasz S The SO(3) instanton homology recently introduced by the authors associates a finite-dimensional vector space over the field of two elements to every embedded trivalent graph (or "web"). The present paper establishes a skein exact triangle for this instanton homology, as well as a realization of the octahedral axiom. From the octahedral diagram, one can derive equivalent reformulations of the authors' conjecture that, for planar webs, the rank of the instanton homology is equal to the number of Tait colorings. National Science Foundation (U.S.) (Grant DMS-0805841) National Science Foundation (U.S.) (Grant DMS-1406348) 2018-05-31T13:53:56Z 2018-05-31T13:53:56Z 2016-05 2018-05-29T16:43:41Z Article http://purl.org/eprint/type/JournalArticle 1753-8416 1753-8424 http://hdl.handle.net/1721.1/116014 Kronheimer, P. B., and T. S. Mrowka. “Exact Triangles for SO(3) Instanton Homology of Webs.” Journal of Topology 9, 3 (May 2016): 774–796 © 2016 London Mathematical Society https://orcid.org/0000-0001-9520-6535 http://dx.doi.org/10.1112/JTOPOL/JTW010 Journal of Topology Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Kronheimer, P. B. Mrowka, Tomasz S Exact Triangles for SO(3) Instanton Homology of Webs |
| title | Exact Triangles for SO(3) Instanton Homology of Webs |
| title_full | Exact Triangles for SO(3) Instanton Homology of Webs |
| title_fullStr | Exact Triangles for SO(3) Instanton Homology of Webs |
| title_full_unstemmed | Exact Triangles for SO(3) Instanton Homology of Webs |
| title_short | Exact Triangles for SO(3) Instanton Homology of Webs |
| title_sort | exact triangles for so 3 instanton homology of webs |
| url | http://hdl.handle.net/1721.1/116014 https://orcid.org/0000-0001-9520-6535 |
| work_keys_str_mv | AT kronheimerpb exacttrianglesforso3instantonhomologyofwebs AT mrowkatomaszs exacttrianglesforso3instantonhomologyofwebs |