Khovanov’s homology for tangles and cobordisms

Bar-Natan, Dror¹

¹ Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3, Canada

Geometry & topology, Tome 9 (2005) no. 3, pp. 1443-1499.

Résumé

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 pictures a little longer than in other articles on the subject, the required extension becomes essentially tautological. And then a simple application of an appropriate functor (a “TQFT”) to our pictures takes them to the familiar realm of complexes of (graded) vector spaces and ordinary homological invariants.

Détail

DOI : 10.2140/gt.2005.9.1443

Keywords: 2–knots, canopoly, categorification, cobordism, Euler characteristic, Jones polynomial, Kauffman bracket, Khovanov, knot invariants, movie moves, planar algebra, skein modules, tangles, trace groups

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