2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78558We 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.amstex, 28 pages with 10 figures. Results in Section 5 are substantially improvedGeometric Topologytext