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I've Computed Kh(T(9,5)) and I'm Happy
February 13, 2005
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
Why am I happy?
- I just barely cleared the fence at the end of the runway.
- It's way out of range of previous techniques/programs.
- It's been three years in the making!
- It took theory, not just labor.
- It proves my local Khovanov theory "right".
- The result seems interesting.
- 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?
- The technique can be generalized to all known Khovanov homology
variants (excluding Khovanov-Rozansky).
- Mikhail Khovanov is no longer perpendicular to My Computer!
Why am I somber?
- I was happy on Wednesday. Mathematicians are never happy straight
- The implementation is pathetic!
- There still are bugs in the program.
- No "testing kit" for the program yet.
- There's a chance the Results are wrong.
- What I'd really like is to truly understand Khovanov-Rozansky
Homology. This is as far as it had ever been.
36 Torus Knots.
See also: My paper
Khovanov's Homology for Tangles