Links, quantum groups and TQFTs

@article{Sawin1995LinksQG,
  title={Links, quantum groups and TQFTs},
  author={S. Sawin},
  journal={Bulletin of the American Mathematical Society},
  year={1995},
  volume={33},
  pages={413-445}
}
  • S. Sawin
  • Published 1995
  • Mathematics, Physics
  • Bulletin of the American Mathematical Society
  • 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… CONTINUE READING
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    References

    SHOWING 1-10 OF 165 REFERENCES
    Quantum Invariants of Knots and 3-Manifolds
    • 1,251
    • PDF
    THE QUANTUM G2 LINK INVARIANT
    • 68
    • PDF
    The quantum G_2 link invariant
    • 24
    • PDF
    Quantum field theory and the Jones polynomial
    • 3,852
    • PDF
    Invariants of 3-manifolds via link polynomials and quantum groups
    • 1,252
    • Highly Influential
    Quantum Groups
    • 4,281
    On the Vassiliev knot invariants
    • 893
    • PDF
    Knots And Physics
    • 641