Estimating a skein module with 𝑆𝐿₂(ℂ) characters

Author:

Bullock Doug

Abstract

We introduce a new technique for estimating the number of generators of the Kauffman bracket skein module of a three manifold; one which requires the construction of linear functionals on a simpler version of the module. Of particular interest is the use of representations of the fundamental group into S L 2 ( C ) SL_2(\hspace {-.3pt}{\mathbb C}\hspace {.3pt}) to generate the functionals.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference8 articles.

1. J. W. Barrett, Skein spaces and spin structures, preprint.

2. D. Bullock, The (2,∞)-skein module of the complement of a (2,2𝑝+1) torus knot, J. Knot Theory Ramifications, 4 no. 4 (1995) 619–632.

3. \bysame, On the Kauffman bracket skein module of surgery on a trefoil, Pacific J. Math., to appear.

4. Varieties of group representations and splittings of 3-manifolds;Culler, Marc;Ann. of Math. (2),1983

5. The (2,∞)-skein module of lens spaces; a generalization of the Jones polynomial;Hoste, Jim;J. Knot Theory Ramifications,1993

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