Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-02-01

Journal: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals: Scopus、SCIE

Volume: 27

Issue: 2

ISSN: 0218-2165

Key Words: Knot invariant; knot polynomial; skein relation; diamond lemma

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.