Rings of $SL_2({\mathbb C})$-Characters and the Kauffman Bracket Skein Module
Abstract
Description
Let $M$ be a compact orientable 3-manifold. The set of characters of $SL_2({\mathbb C})$ representations of the fundamental group of $M$ forms a closed affine algebraic set. We show that its coordinate ring is isomorphic to a specialization of the Kauffman bracket skein module modulo its nilradical. This is accomplished by making the module into a combinatorial analog of the ring, in which tools of skein theory are exploited to illuminate relations among characters. We conclude with an application, proving that a small manifold's specialized module is necessarily finite dimensional.
LaTeX2e v1.2, document class amsart.cls with package epsfig, 18 pages, 9 figures
LaTeX2e v1.2, document class amsart.cls with package epsfig, 18 pages, 9 figures