Knot invariant with multiple skein relations
Geometric Topology
2017-03-20 v1
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 invariant. 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
Cite
@article{arxiv.1703.05911,
title = {Knot invariant with multiple skein relations},
author = {Zhiqing Yang},
journal= {arXiv preprint arXiv:1703.05911},
year = {2017}
}
Comments
24 pages, 5 figures. arXiv admin note: text overlap with arXiv:1004.2085