Knot invariants from symbolic dynamical systems

If is the group of an oriented knot , then the set of representations of the commutator subgroup into any finite group has the structure of a shift of finite type , a special type of dynamical system completely described by a finite directed graph. Invariants of , such as its topological entropy or the number of its periodic points of a given period, determine invariants of the knot. When is abelian, gives information about the infinite cyclic cover and the various branched cyclic covers of . Similar techniques are applied to oriented links.