Chern-Simons theory in mathematics, condensed matter theory and cosmology

Abstract

Various applications of Chern-Simons theory in algebraic topology, in particular knot theory, condensed matter physics and cosmology are reviewed. Special attention is paid to appearances of Chern-Simons actions in the theory of the (integer and fractional) quantum Hall effect. A mechanism related to five-dimensional abelian Chern-Simons theory that may be at the origin of the observed intergalactic magnetic fields in the universe is described.