On 2-Adjacency Between Links

Citation:

Zhixiong TAO.On 2-Adjacency Between Links[J].Chinese Annals of Mathematics B,2016,37(5):767~776
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Authors:

Zhixiong TAO;

Foundation:

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (No.LY12A01025).
Abstract: The author discusses 2-adjacency of two-component links and study the relations between the signs of the crossings to realize 2-adjacency and the coefficients of the Conway polynomial of two related links. By discussing the coefficient of the lowest $m$ power in the Homfly polynomial, the author obtains some results and conditions on whether the trivial link is 2-adjacent to a nontrivial link, whether there are two links 2-adjacent to each other, etc. Finally, this paper shows that the Whitehead link is not 2-adjacent to the trivial link, and gives some examples to explain that for any given two-component link, there are infinitely many links 2-adjacent to it. In particular, there are infinitely many links 2-adjacent to it with the same Conway polynomial.

Keywords:

2-Adjacency, Link, Conway polynomial, Jones polynomial, Homfly polynomial

Classification:

57M25
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