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Topological quantum field theory.
9
votes
Usefulness of using TQFTs
The Tait flyping conjecture was proven by Menasco and Thistlethwaite using knot polynomial invariants (which are a version of TQFT invariants).
There is a lower bound on the braid index of a knot in …
9
votes
Accepted
Is the instanton homology for webs and foams a categorified Chern-Simons?
It’s not clear what you mean by categorify here: the J# invariant doesn’t have a grading in their definition. Just taking dimension to get a number then doesn’t seem to yield a polynomial invariant.
…
5
votes
How many definitions are there of the Jones polynomial?
Bigelow (after Lawrence) gave a homological definition of the Jones polynomial in terms of a plat representation. Lawrence identified the Jones representations as representations associated to braid g …