Achirality of knots and links

Boju Jiang; Xiao-Song Lin; Shicheng Wang; Ying-Qing Wu

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arXiv · math/9905158

Achirality of knots and links

Boju Jiang·Xiao-Song Lin·Shicheng Wang·Ying-Qing Wu

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Abstract

We will develop various methods, some are of geometric nature and some are of algebraic nature, to detect the various achiralities of knots and links in $S^3$. For example, we show that the twisted Whitehead double of a knot is achiral if and only if the double is the unknot or the figure eight knot, and we show that all non-trivial links with $\leq9$ crossings are not achiral except the Borromean rings. A simple procedure for calculating the $η$-function is given in terms of a crossing change formula and its initial values.

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BibTeX RIS

Boju Jiang, Xiao-Song Lin, Shicheng Wang, Ying-Qing Wu. 1999-06-29. Achirality of knots and links. https://arxiv.org/abs/math/9905158

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