Algebraic Dynamics of Knots and Links

University Of South Alabama, Mobile AL

Investigators

Abstract

DMS-0071004 Daniel S. Silver and Susan G. Williams Knot theory applications from a newly emerging area of dynamics, the study of dynamical systems of algebraic origin, will be developed. The set of representations into a compact group of the derived group of a link group will be studied as a dynamical system. New results about knot symmetries and branched covers of links are expected. A recently discovered relationship between symbolic dynamical systems and topological quantum field theory will be explored. The research will address open questions in knot theory and dynamics and expand on previous results in these fields. It will continue a new program of research in knot theory that incorporates ideas from symbolic dynamical systems. The investigation of knots and links has attracted great attention not only in the mathematical world but also in the larger scientific community. Knotting and linking phenomena are found in molecular biology and plasma physics, for example, while striking similarites in computational methods arise frequently in theoretical physics. The proposed research will provide new understanding of knots and links by using techniques from symbolic dynamical systems, a mathematical branch of information theory. The research will also strengthen interaction between researchers in the fields of topology and dynamics.