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.
arXiv Mathematics e-prints
- Pub Date:
- October 2004
- Mathematics - Geometric Topology;
- Mathematics - Quantum Algebra;
- Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper33.abs.html