On 2-Adjacency Between Links |
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Authors: | Zhixiong TAO |
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Institution: | Department of Mathematics, School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, China |
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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. |
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Keywords: | 2-Adjacency Link Conway polynomial Jones polynomial Homfly
polynomial |
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