Understanding the Kauffman bracket skein module

Abstract

The Kauffman bracket skein module $K(M)$ of a 3-manifold $M$ is defined over formal power series in the variable $h$ by letting $A=e^{h/4}$. For a compact oriented surface $F$, it is shown that $K(F\times I)$ is a quantization of the $\g$-characters of the fundamental group of $F$, corresponding to a geometrically defined Poisson bracket. Finite type invariants for unoriented knots and links are defined. Topologically free Kauffman bracket modules are shown to generate finite type invariants. It is shown for compact $M$ that $K(M)$ can be generated as a module by cables on a finite set of knots. Moreover, if $M$ contains no incompressible surfaces, the module is finitely generated.

LaTeX2e v1.2, customized document class jktr.cls (included), requires packages epsfig and amstex, 13 pages, 26 figures inserted repeatedly

References in corpus (2)

• Two dimensional lattice gauge theory based on a quantum group
• Link Invariants and Combinatorial Quantization of Hamiltonian Chern-Simons Theory

Cited by in corpus (1)

• Chebyshev polynomials and the Frohman-Gelca formula