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On 2-adjacency between links

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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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Author information

Correspondence to Zhixiong Tao.

Additional information

This work was supported by the Zhejiang Provincial Natural Science Foundation of China (No. LY12A01025).

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Cite this article

Tao, Z. On 2-adjacency between links. Chin. Ann. Math. Ser. B 37, 767–776 (2016). https://doi.org/10.1007/s11401-016-1014-0

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Keywords

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

2000 MR Subject Classification

  • 57M25