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

I've Computed Kh(T(9,5)) and I'm Happy

February 13, 2005
Knots in Washington XX
A Conference in honour of Lou Kauffman's 60th Birthday
George Washington University

Abstract. I'm also very tired, and there may still be bugs in the program.

Why am I happy?

  1. I just barely cleared the fence at the end of the runway.
  2. It's way out of range of previous techniques/programs.
  3. It's been three years in the making!
  4. It took theory, not just labor.
  5. It proves my local Khovanov theory "right".
  6. The result seems interesting.
  7. A whole new universe of knots is now accessible - cables, Whitehead doubles, etc. The old phenomenology lead to phenomenal results. Who knows where that will go?
  8. The technique can be generalized to all known Khovanov homology variants (excluding Khovanov-Rozansky).
  9. Mikhail Khovanov is no longer perpendicular to My Computer!
Why am I somber?

  1. I was happy on Wednesday. Mathematicians are never happy straight for long.
  2. The implementation is pathetic!
  3. There still are bugs in the program.
  4. No "testing kit" for the program yet.
  5. There's a chance the Results are wrong.
  6. What I'd really like is to truly understand Khovanov-Rozansky Homology. This is as far as it had ever been.

Handouts: The Results, FastKh.pdf.
Transparencies: Bracket.pdf (Bracket.nb), Categorification.m, 36 Torus Knots.
See also: My paper Khovanov's Homology for Tangles and Cobordisms.