SYMMETRY GROUPS OF HYPERBOLIC KNOTS AND LINKS

Canonical triangulations provide an algorithm to compute the symmetry groups of hyperbolic links and their complements, along with information on how each symmetry acts on the link components. The latter information determines the chirality and invertibility of the link. Symmetry groups of knots to ten crossings and multicomponent hyperbolic links to nine crossing are listed, with some exceptions. A Macintosh computer program, available free of charge, computes symmetry groups interactively.