The skein index for link invariants

Abstract

We introduce the skein index, which is an integer-valued index of a link invariant. It is used to compare link invariants and to find a skein relation. We give the complete list for link invariants of skein index less than or equal to two, and discuss the skein indices of operator invariants, and in particular quantum invariants and quandle coloring numbers. By determining the skein index of the JKSS invariant, we construct a new skein relation and give a formula for the invariant of a closed 2-braid.