Published December 22, 2005
| Submitted
Discussion Paper
Open
Matrix Factorizations and Kauffman Homology
- Creators
-
Gukov, Sergei
- Walcher, Johannes
Chicago
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Abstract
The topological string interpretation of homological knot invariants has led to several insights into the structure of the theory in the case of sl(N). We study possible extensions of the matrix factorization approach to knot homology for other Lie groups and representations. In particular, we introduce a new triply graded theory categorifying the Kauffman polynomial, test it, and predict the Kauffman homology for several simple knots.
Additional Information
We would like to thank M. Khovanov, M. Mariño, C. Vafa, and E. Witten for valuable discussions. We are grateful to the KITP, Santa Barbara for warm hospitality during the program "Mathematical Structures in String Theory", where part of this work was carried out. This work was conducted during the period S.G. served as a Clay Mathematics Institute Long-Term Prize Fellow. This work was also supported in part by the DOE under grant number DE-FG02-90ER40542, in part by RFBR grant 04-02-16880 and in part by the NSF under Grant No. PHY99-07949.Attached Files
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Additional details
- Eprint ID
- 66979
- Resolver ID
- CaltechAUTHORS:20160511-092422859
- Department of Energy (DOE)
- DE-FG02-90ER40542
- Russian Foundation for Basic Research
- 04-02-16880
- NSF
- PHY99-07949
- Clay Mathematics Institute
- Created
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2016-05-11Created from EPrint's datestamp field
- Updated
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2023-06-01Created from EPrint's last_modified field