Colored Kauffman Homology and Super-A-polynomials
Abstract
We study the structural properties of colored Kauffman homologies of knots. Quadruple-gradings play an essential role in revealing the differential structure of colored Kauffman homology. Using the differential structure, the Kauffman homologies carrying the symmetric tensor products of the vector representation for the trefoil and the figure-eight are determined. In addition, making use of relations from representation theory, we also obtain the HOMFLY homologies colored by rectangular Young tableaux with two rows for these knots. Furthermore, the notion of super-A-polynomials is extended in order to encompass two-parameter deformations of PSL(2,C) character varieties.
Cite
@article{arxiv.1310.2240,
title = {Colored Kauffman Homology and Super-A-polynomials},
author = {Satoshi Nawata and P. Ramadevi and Zodinmawia},
journal= {arXiv preprint arXiv:1310.2240},
year = {2014}
}
Comments
47+21 pages, 17 figures, 5 tables; Ancillary file attached on the right; v2,v3,v4 minor corrections and references added