Tait colorings, and an instanton homology for webs and foams
We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. We prove a non-vanishing theorem for this SO(3) instanton homology of webs, using Gabai’s sutured manifold theory. It is hope...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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European Mathematical Society Publishing House
2020
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| Online Access: | https://hdl.handle.net/1721.1/127673 |
| _version_ | 1826196024726650880 |
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| author | Kronheimer, Peter Mrowka, Tomasz S |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kronheimer, Peter Mrowka, Tomasz S |
| author_sort | Kronheimer, Peter |
| collection | MIT |
| description | We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. We prove a non-vanishing theorem for this SO(3) instanton homology of webs, using Gabai’s sutured manifold theory. It is hoped that the non-vanishing theorem may support a program to provide a new proof of the four-color theorem. |
| first_indexed | 2024-09-23T10:19:37Z |
| format | Article |
| id | mit-1721.1/127673 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:19:37Z |
| publishDate | 2020 |
| publisher | European Mathematical Society Publishing House |
| record_format | dspace |
| spelling | mit-1721.1/1276732022-09-30T20:24:05Z Tait colorings, and an instanton homology for webs and foams Kronheimer, Peter Mrowka, Tomasz S Massachusetts Institute of Technology. Department of Mathematics We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. We prove a non-vanishing theorem for this SO(3) instanton homology of webs, using Gabai’s sutured manifold theory. It is hoped that the non-vanishing theorem may support a program to provide a new proof of the four-color theorem. NSF (Grants DMS-0805841 and DMS-1406348) 2020-09-21T21:55:46Z 2020-09-21T21:55:46Z 2018-09 2019-11-18T14:39:30Z Article http://purl.org/eprint/type/JournalArticle 1435-9855 https://hdl.handle.net/1721.1/127673 Kronheimer, Peter and Tomasz Mrowka. "Tait colorings, and an instanton homology for webs and foams." Journal of the European Mathematical Society 21, 1 (September 2018): 55-119 © 2019 European Mathematical Society en http://dx.doi.org/10.4171/jems/831 Journal of the European Mathematical Society Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf European Mathematical Society Publishing House other univ website |
| spellingShingle | Kronheimer, Peter Mrowka, Tomasz S Tait colorings, and an instanton homology for webs and foams |
| title | Tait colorings, and an instanton homology for webs and foams |
| title_full | Tait colorings, and an instanton homology for webs and foams |
| title_fullStr | Tait colorings, and an instanton homology for webs and foams |
| title_full_unstemmed | Tait colorings, and an instanton homology for webs and foams |
| title_short | Tait colorings, and an instanton homology for webs and foams |
| title_sort | tait colorings and an instanton homology for webs and foams |
| url | https://hdl.handle.net/1721.1/127673 |
| work_keys_str_mv | AT kronheimerpeter taitcoloringsandaninstantonhomologyforwebsandfoams AT mrowkatomaszs taitcoloringsandaninstantonhomologyforwebsandfoams |