Achirality of knots and links

Details Achirality of knots and links Achirality of knots and links

1999-05-25

arxiv.org/abs/math/9905158v2

Mathematics

Geometric Topology

amstex, 28 pages with 10 figures. Results in Section 5 are substantially improved

Scientific paper

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 $\eta$-function is given in terms of a crossing change formula and its initial values.

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