Links, quantum groups and TQFTs
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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 frameworks 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 and proven to be invariant.References
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Additional Information
- Stephen Sawin
- Affiliation: Department of Mathematics, Room 2-265, Massachusetts Institute of Technology, Cambridge, MA 02139-4307
- Address at time of publication: Bannow 105, Department of Mathematics, Fairfield University, Fairfield, CT 06430-5195
- Email: sawin@math.mit.edu, ssawin@fair1.fairfield.edu
- Received by editor(s): April 5, 1995
- Additional Notes: This research supported in part by NSF postdoctoral Fellowship #23068.
- © Copyright 1996 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 33 (1996), 413-445
- MSC (1991): Primary 57M25; Secondary 16W30, 57M30
- DOI: https://doi.org/10.1090/S0273-0979-96-00690-8
- MathSciNet review: 1388838