© | << < ? > >> | Dror Bar-Natan: Talks:

Knot Invariants from Finite Dimensional Integration

International Congress of Basic Science, Beijing, July 2024.

Abstract. For the purpose of today, an "I-Type Knot Invariant" is a knot invariant computed from a knot diagram by integrating the exponential of a pertubed Gaussian Lagrangian which is a sum over the features of that diagram (crossings, edges, faces) of locally defined quantities, over a product of finite dimensional spaces associated to those same features.

Q. Are there any such things?
A. Yes.

Q. Are they any good?
A. They are the strongest we know per CPU cycle, and are excellent in other ways too.

Q. Didn't Witten do that back in 1988 with path integrals?
A. No. His constructions are infinite dimensional and far from rigorous.

Q. But integrals belong in analysis!
A. Ours only use squeaky-clean algebra.

URL: http://drorbn.net/icbs24.

Links: AKT AP BG Cars DPG Ov

Handout: IType.html, IType.pdf.

Talk Video@YouTube (not yet available).

Talk Video on drorbn.net (not yet available).

Sources: pensieve.