Links, Quantum Groups, and TQFT's
Abstract
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.
 Publication:

eprint arXiv:qalg/9506002
 Pub Date:
 June 1995
 arXiv:
 arXiv:qalg/9506002
 Bibcode:
 1995q.alg.....6002S
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory
 EPrint:
 Expository/Survey. 36 pages, AMSLaTeX with psfig, *many* ps figures included via uufiles. PS file available at ftp://ftpmathpapers.mit.edu/Sawin/Sawin4.ps or http://web.mit.edu/org/m/mathdept/www/ . Unchanged except for commands to correct tex problems