On Khovanov's categorification of the Jones polynomial

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.Comment: 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 fil

Categorification of the colored sl3\mathfrak{sl}_3-invariant

We give explicit resolutions of all finite dimensional, simple $U_q(\mathfrak{sl_3})$-modules. We use these resolutions to categorify the colored $\mathfrak{sl}_3$-invariant of framed links via a complex of complexes of graded $\mathbb{Z}$-modules.Comment: 39 pages, many figures. Comments welcome