Colored Kauffman Homology and Super-A-polynomials

Understand

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.