Doug Bullock
The Kauffman bracket skein module is an algebraic invariant of three manifolds which encodes invariants of links in manifolds as well. In certain cases the module is an algebra; in fact, a quantum deformation of a finitely generated commutative algebra. It seems seems very likely that the undeformed algeba is the ring of $SL_2(F)$ characters of the fundamental group. We will discuss the theorems and examples that make this conjecture plausible, as well as their applications in skein theory, character theory, and topological quantum field theory.