Let M be a compact orientable 3-manifold. The set of characters of SL2()-representations of 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 realizing the module as 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.
Cite this article
D. Bullock, Rings of SL2( )-characters and the Kauffman bracket skein module. Comment. Math. Helv. 72 (1997), no. 4, pp. 521–542DOI 10.1007/S000140050032