On Khovanov's categorification of the Jones polynomial
Dror Bar-Natan
Abstract
The working mathematician fears complicated words but loves pictures and diagrams. We thus give a no-fancy-anything picture rich glimpse into Khovanov's novel construction of `the categorification of the Jones polynomial'. For the same low cost we also provide some computations, including one that shows that Khovanov's invariant is strictly stronger than the Jones polynomial and including a table of the values of Khovanov's invariant for all prime knots with up to 11 crossings.
arXiv comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-16.abs.html, 34 pages with many figures, source contains associated program and data file
I want to clarify, I am not trivializing the work of category theorist. It is a field of mathematics which provides a useful framework for algebraic geometers and algebraic topologists, and has even been fruitfully applied outside of math. A personal favorite of CT generalizing…
Courses would benefit from "quick-reference guides like the end of Dror Bar Natan's paper on Khovanov homology http://arxiv.org/abs/math/0201043 He says "It can fit inside your wallet." See: http://www.math.toronto.edu/drorbn/Talks/HUJI-011104/cube.gi...
I want to clarify, I am not trivializing the work of category theorist. It is a field of mathematics which provides a useful framework for algebraic geometers and algebraic topologists, and has even been fruitfully applied outside of math. A personal favorite of CT generalizing…
throw_away_8080View on HNParent context