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2006 The Karoubi envelope and Lee's degeneration of Khovanov homology
Dror Bar-Natan, Scott Morrison
Algebr. Geom. Topol. 6(3): 1459-1469 (2006). DOI: 10.2140/agt.2006.6.1459

Abstract

We give a simple proof of Lee’s result from [Adv. Math. 179 (2005) 554–586], that the dimension of the Lee variant of the Khovanov homology of a 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.

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Dror Bar-Natan. Scott Morrison. "The Karoubi envelope and Lee's degeneration of Khovanov homology." Algebr. Geom. Topol. 6 (3) 1459 - 1469, 2006. https://doi.org/10.2140/agt.2006.6.1459

Information

Received: 29 June 2006; Accepted: 20 July 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1130.57012
MathSciNet: MR2253455
Digital Object Identifier: 10.2140/agt.2006.6.1459

Subjects:
Primary: 57M25
Secondary: 18E05, 57M27

Rights: Copyright © 2006 Mathematical Sciences Publishers

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