© | Dror Bar-Natan: Publications:

The Karoubi Envelope and Lee's Degeneration of Khovanov Homology

joint with Scott Morrison.

last updated June 28, 2006
first edition: June 21, 2006
Algebraic & Geometric Topology 6 (2006) 1459-1469

We give a simple proof of Lee's result from arXiv:math.GT/0210213, that the dimension of the Lee variant of the Khovanov homology of an c-component link is 2c, regardless of the number of crossings. Our method of proof is entirely local and hence we can state a Lee-type theorem for tangles as well as for knots and links. Our main tool is the "Karoubi envelope of the cobordism category", a certain enlargement of the cobordism category which is mild enough so that no information is lost yet strong enough to allow for some simplifications that are otherwise unavailable.

The paper. karoubi.pdf, karoubi.ps, SVN source, arXiv:math.GT/0606542.

Published version. Algebraic & Geometric Topology 6 (2006) 1459-1469.

Also see my earlier paper on the subject, "Khovanov's Homology for Tangles and Cobordisms".