Khovanov's homology for tangles and cobordisms

Abstract

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.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper33.abs.html

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