Multiplicative structure of Kauffman bracket skein module quantizations
Authors:
Doug Bullock and Józef H. Przytycki
Journal:
Proc. Amer. Math. Soc. 128 (2000), 923931
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 fourpunctured sphere and twicepunctured 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/S0002993999050431
PII:
S 00029939(99)050431
Keywords:
Knot,
link,
3manifold,
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 NSFDMS Postdoctoral Fellowship.
Communicated by:
Ronald A. Fintushel
Article copyright:
© Copyright 1999
American Mathematical Society
