The theory of knot invariants of finite type (Vassiliev invariants) is described. These invariants turn out to be at least as powerful as the Jones polynomial and its numerous generalizations coming… (More)

We give a fresh introduction to the Khovanov Homology theory for knots and links, with special emphasis on its extension to tangles, cobordisms and 2-knots. By staying within a world of topological… (More)

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… (More)

We present the perturbation theory of the Chern-Simons gauge eld theory and prove that to second order it indeed gives knot invariants. We identify these invariants and show that in fact we get a… (More)

DROR BAR-NATAN AND STAVROS GAROUFALIDIS This is a pre-preprint. Corrections, suggestions, reservations and donations are more than welcome! Abstract. We prove a conjecture stated by Melvin and Morton… (More)

We continue the work started in [Å-I], and prove the invariance and universality in the class of finite type invariants of the object defined and motivated there, namely the Århus integral of… (More)

We investigate Vassiliev homotopy invariants of string links, and find that in this particular case, most of the questions left unanswered in [3] can be answered affirmatively. In particular,… (More)

Given a representation of a Lie algebra and an ad-invariant bilinear form we show how to assign numerical weights to a certain collection of graphs. This assignment is then shown to satisfy certain… (More)

We introduce a local algorithm for Khovanov Homology computations — that is, we explain how it is possible to “cancel” terms in the Khovanov complex associated with a (“local”) tangle, hence… (More)

Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [5, 9], which give, respectively, the exact Kontsevich integral of… (More)