The Karoubi envelope and Lee's degeneration of Khovanov homology
Abstract
We give a simple proof of Lee's result from [Adv. Math. 179 (2005) 554586; arXiv:math.GT/0210213], that the dimension of the Lee variant of the Khovanov homology of a ccomponent link is 2^c, regardless of the number of crossings. Our method of proof is entirely local and hence we can state a Leetype 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606542
 Bibcode:
 2006math......6542B
 Keywords:

 Mathematics  Geometric Topology;
 57M25;
 18E05;
 57M27
 EPrint:
 This is the version published by Algebraic &