Abstract
The well-known technique of n-coloring a diagram of an oriented link l is generalized using elements of the circle T for colors. For any positive integer 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 T r−1 . The set of ( T , r )-colorings of D is an abelian group, and its quotient by the connected component 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 link l. Results about braid entropy are obtained using techniques of symbolic dynamical systems.
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