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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 …
Ian Agol's user avatar
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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. …
Ian Agol's user avatar
  • 68.8k
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 …
Ian Agol's user avatar
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