Symbolic dynamics and symmetries of knots
by
Susan Williams
University of South Alabama
Coauthors: Daniel Silver

Given an oriented knot or link l and a finite group \Sigma, we define a shift of finite type called the representation shift of l in \Sigma. Its conjugacy class is a link invariant. The periodic point structure of the representation shift yields restrictions on the possible periods of symmetries of the link. We can also associate to a braid B (or, more generally, to a tangle) a 2-dinensional shift of finite type that gives information about the family of links formed by the closures of Bⁿ.

Date received: March 10, 1998