Links, Quantum Groups, and TQFT's
Stephen Sawin

TL;DR
This paper explores the construction of knot invariants like the Jones polynomial via quantum groups and tangle functors, and develops related 3-manifold invariants and topological quantum field theories.
Contribution
It explicitly constructs the quantum group U_q(sl_2) and links it to knot invariants and TQFTs, providing a unified formalism for these concepts.
Findings
Constructed the Jones polynomial and Kauffman bracket
Developed quantum group and tangle functor formalisms
Built 3-manifold invariants and TQFTs from link invariants
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 , which gives rise to the Jones polynomial, is constructed explicitly. The -manifold invariants and the axiomatic topological quantum field theories which arise from these link invariants at certain values of the parameter are constructed.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsQuantum Mechanics and Applications · Logic, programming, and type systems · Algebraic structures and combinatorial models
