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 *2 ^{c}*, 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".