Links, Quantum Groups, and TQFT's

Details Links, Quantum Groups, and TQFT's Links, Quantum Groups, and TQFT's

1995-06-02

arxiv.org/abs/q-alg/9506002v2

Physics

High Energy Physics

High Energy Physics - Theory

Expository/Survey. 36 pages, AMSLaTeX with psfig, *many* ps figures included via uufiles. PS file available at ftp://ftp-mat

Scientific paper

The Jones polynomial and the Kauffman bracket are constructed, and their relation with knot and link theory is described. The quantum groups and tangle functor formalisms for understanding these invariants and their descendents are given. The quantum group $U_q(sl_2)$, which gives rise to the Jones polynomial, is constructed explicitly. The $3$-manifold invariants and the axiomatic topological quantum field theories which arise from these link invariants at certain values of the parameter are constructed.

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