Coloring link diagrams with a continuous palette

The well-known technique of n-coloring a diagram of an oriented link I is g eneralized using elements of the circle T for colors. For any positive inte ger r, the more general notion of a (T, r)-coloring is defined by labeling the arcs of a diagram D with elements of the torus Tr-1. The set of (T, r)- colorings of D is an abelian group, and its quotient by the connected compo nent of the identity is isomorphic to the torsion subgroup of H-1 (M-r(l); Z). Here M-r(l) denotes the r-fold cyclic cover of S-3 branched over the li nk l. Results about braid entropy are obtained using techniques of symbolic dynamical systems. (C) 2000 Elsevier Science Ltd. All rights reserved.