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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

Links, quantum groups and TQFTs


Author: Stephen Sawin
Journal: Bull. Amer. Math. Soc. 33 (1996), 413-445
MSC (1991): Primary 57M25; Secondary 16W30, 57M30
MathSciNet review: 1388838
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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.


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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

DOI: http://dx.doi.org/10.1090/S0273-0979-96-00690-8
PII: S 0273-0979(96)00690-8
Keywords: Cobordisms, Hopf algebras, Jones polynomial, knots, link invariants, quantum groups, tangles, three-manifolds, topological quantum field theory
Received by editor(s): April 5, 1995
Additional Notes: This research supported in part by NSF postdoctoral Fellowship #23068.
Article copyright: © Copyright 1996 American Mathematical Society