Geodesic
sl(2) tangle homology with a parameter and singular cobordisms
Caprau, Carmen Livia1
1Department of Mathematics, California State University, 5245 North Backer Avenue M/S PB 108, Fresno CA 93740-8001, USA
Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 729-756
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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.

DOI : 10.2140/agt.2008.8.729
Keywords: categorification, cobordisms, Euler characteristic, Jones polynomial, functoriality, Khovanov homology, knots and links, movie moves, webs and foams

Caprau, Carmen Livia  1

1 Department of Mathematics, California State University, 5245 North Backer Avenue M/S PB 108, Fresno CA 93740-8001, USA 
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Caprau, Carmen Livia. sl(2) tangle homology with a parameter and singular cobordisms. Algebraic and Geometric Topology, Tome 8 (2008) no. 2, pp. 729-756. doi: 10.2140/agt.2008.8.729

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