2017/03/10 by Kauffman, Louis H., Lambropoulou, Sofia
#57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT)
paper · doi:10.48550/arxiv.1703.03655
We introduce new skein invariants of links based on a procedure where we first apply the skein relation only to crossings of distinct components, so as to produce collections of unlinked knots. We then evaluate the resulting knots using a given invariant. A skein invariant can be computed on each link solely by the use of skein relations and a set of initial conditions. The new procedure, remarkably, leads to generalizations of the known skein invariants. We make skein invariants of classical links, H[R], K[Q] and D[T], based on the invariants of knots, R, Q and T, denoting the regular isotopy version of the Homflypt polynomial, the Kauffman polynomial and the Dubrovnik polynomial. We provide skein theoretic proofs of the well-definedness of these invariants. These invariants are also reformulated into summations of the generating invariants (R, Q, T) on sublinks of a given link L, obtained by partitioning L into collections of sublinks.