Title: Multiplicative structure of Kauffman bracket skein module quantizations

Authors:  Doug Bullock and Jozef H. Przytycki

Preprint: GWUM-1999-08 

Abstract: We describe, for a few small examples, the Kauffman bracket skein algebra of a surface crossed with an interval. If the surface is a punctured torus the result is a quantization of the symmetric algebra in three variables (and an algebra closely related to a cyclic quantization of U(so(3)). For a torus without boundary we obtain a quantization of ``the symmetric homologies" of a torus (equivalently, the coordinate ring of the SL(2,C)-character variety of Z oplus Z). Presentations are also given for the four punctured sphere and twice punctured torus. We conclude with an investigation of central elements and zero divisors.

Note: to appear in PAMS.