Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published May 11, 2016 | Submitted
Report Open

Matrix Factorizations and Kauffman Homology

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. MariƱo, 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

Submitted - 0512298.pdf

Files

0512298.pdf
Files (415.5 kB)
Name Size Download all
md5:e56f56e4f5bfcd88ac279a0317c7094a
415.5 kB Preview Download

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023