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2-Adjacency between knots

Zhi-Xiong Tao

School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, P. R. China

https://doi.org/10.1142/S0218216515500546Cited by:5 (Source: Crossref)

Abstract

We study the properties of a knot K to be 2-adjacent to another knot W by analyzing their Conway polynomials, Jones polynomials and Homfly polynomials and give some very useful conditions. We discuss whether each pair of knots can be 2-adjacent to each other, i.e. whether 2-adjacency is a symmetric relation. We discuss also whether the trivial knot, the trefoil knot and the figure-eight knot can be 2-adjacent to any knot in Rolfsen's table and the opposite cases, except for 9₃₄ it is not decided whether it is 2-adjacent to 4₁. Finally, we give some examples to answer I. Torisu's problem partly and etc.

Keywords:

AMSC: 57M25

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