Multiplicative structure of Kauffman bracket skein module quantizations

Authors:
Doug Bullock and Józef H. Przytycki

Journal:
Proc. Amer. Math. Soc. **128** (2000), 923-931

MSC (1991):
Primary 57M99

Published electronically:
July 28, 1999

MathSciNet review:
1625701

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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 )). For a torus without boundary we obtain a quantization of ``the symmetric homologies" of a torus (equivalently, the coordinate ring of the -character variety of ). Presentations are also given for the four-punctured sphere and twice-punctured torus. We conclude with an investigation of central elements and zero divisors.

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Additional Information

**Doug Bullock**

Affiliation:
Department of Mathematics, The George Washington University, Washington, DC 20052

Address at time of publication:
Department of Mathematics, University of Maryland, College Park, Maryland 20742

Email:
bullock@math.umd.edu

**Józef H. Przytycki**

Affiliation:
Department of Mathematics, The George Washington University, Washington, DC 20052

Email:
przytyck@math.gwu.edu

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-05043-1

Keywords:
Knot,
link,
3-manifold,
skein module

Received by editor(s):
November 17, 1997

Received by editor(s) in revised form:
May 5, 1998

Published electronically:
July 28, 1999

Additional Notes:
The first author is supported by an NSF-DMS Postdoctoral Fellowship.

Communicated by:
Ronald A. Fintushel

Article copyright:
© Copyright 1999
American Mathematical Society