Volume 8, issue 2 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
sl(2) tangle homology with a parameter and singular cobordisms

Carmen Livia Caprau

Algebraic & Geometric Topology 8 (2008) 729–756
Abstract

We construct a bigraded cohomology theory which depends on one parameter a, and whose graded Euler characteristic is the quantum sl(2) link invariant. We follow Bar-Natan’s approach to tangles on one side, and Khovanov’s sl(3) theory for foams on the other side. Our theory is properly functorial under tangle cobordisms, and a version of the Khovanov sl(2) invariant (or Lee’s modification of it) corresponds to a = 0 (or a = 1). In particular, the construction naturally resolves the sign ambiguity in the functoriality of Khovanov’s sl(2) theory.

Keywords
categorification, cobordisms, Euler characteristic, Jones polynomial, functoriality, Khovanov homology, knots and links, movie moves, webs and foams
Mathematical Subject Classification 2000
Primary: 57M27, 57M25
Secondary: 18G60
References
Publication
Received: 9 January 2008
Accepted: 28 January 2008
Published: 25 May 2008
Authors
Carmen Livia Caprau
Department of Mathematics
California State University
5245 North Backer Avenue M/S PB 108
Fresno CA 93740-8001
USA
http://zimmer.csufresno.edu/~ccaprau