English

Links, Quantum Groups, and TQFT's

q-alg 2008-02-03 v2 High Energy Physics - Theory Quantum Algebra

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 Uq(sl2)U_q(sl_2), which gives rise to the Jones polynomial, is constructed explicitly. The 33-manifold invariants and the axiomatic topological quantum field theories which arise from these link invariants at certain values of the parameter are constructed.

Keywords

Cite

@article{arxiv.q-alg/9506002,
  title  = {Links, Quantum Groups, and TQFT's},
  author = {Stephen Sawin},
  journal= {arXiv preprint arXiv:q-alg/9506002},
  year   = {2008}
}

Comments

Expository/Survey. 36 pages, AMSLaTeX with psfig, *many* ps figures included via uufiles. PS file available at ftp://ftp-math-papers.mit.edu/Sawin/Sawin4.ps or http://web.mit.edu/org/m/mathdept/www/ . Unchanged except for commands to correct tex problems