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Knot invariants with multiple skein relations

Department of Mathematics, Dalian University of Technology, P. R. China

https://doi.org/10.1142/S0218216518500177Cited by:1 (Source: Crossref)

Abstract

Given any oriented link diagram, one can construct knot invariants using skein relations. Usually such a skein relation contains three or four terms. In this paper, the author introduces several new ways to smooth a crossings, and uses a system of skein equations to construct link invariants. This invariant can also be modified by writhe to get a more powerful invariant. The modified invariant is a generalization of both the HOMFLYPT polynomial and the two-variable Kauffman polynomial. Using the diamond lemma, a simplified version of the modified invariant is given. It is easy to compute and is a generalization of the two-variable Kauffman polynomial.

Keywords:

AMSC: 57M27, 57M25

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