The Karoubi envelope and Lee’s degeneration of Khovanov homology
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Open Access
- 4 October 2006
- journal article
- Published by Mathematical Sciences Publishers in Algebraic & Geometric Topology
- Vol. 6 (3) , 1459-1469
Abstract
We give a simple proof of Lee's result from [Adv. Math. 179 (2005) 554-586; arXiv:math.GT/0210213], that the dimension of the Lee variant of the Khovanov homology of a 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.Comment: This is the version published by Algebraic & Geometric Topology on 4 October 200Keywords
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This publication has 3 references indexed in Scilit:
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