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| On 2-Adjacency Between Links |
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Citation： |
Zhixiong TAO.On 2-Adjacency Between Links[J].Chinese Annals of Mathematics B,2016,37(5):767~776 |
| Page view： 1255
Net amount： 1087 |
Authors： |
Zhixiong TAO; |
Foundation： |
This work was supported by the Zhejiang Provincial
Natural Science Foundation of China (No.LY12A01025). |
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| 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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