The colored HOMFLY homology and super-A-polynomial (Intelligence of Low-dimensional Topology)
Hiroyuki Fuji · Institutional Repositories DataBase (IRDB) · 2013
In this article we will discuss the generalizations of the A-polynomial on basis of the colored superpolynomial.The colored superpolynomial is the Poincar\'e polynomial of the colored HOMFLY homology that categorifies the colored HOMFLY polynomial.In partic- ular for the colored superpolynomial with the symmetric representation, the analogues of the generalized/quantum volume conjecture can be considered.As a result of the study of the colored HOMFLY homology for the $(2, 2p+1)$ -torus knots and $n$ -twist knots, we find the 2-parameter deformation of the A-polynomial that is named as super-$A$ -polynomial.