Geodesic
The universal sl3–link homology
Mackaay, Marco1 ; Vaz, Pedro1
1Departamento de Matemática, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal
Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1135-1169
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We define the universal sl3–link homology, which depends on 3 parameters, following Khovanov’s approach with foams. We show that this 3–parameter link homology, when taken with complex coefficients, can be divided into 3 isomorphism classes. The first class is the one to which Khovanov’s original sl3–link homology belongs, the second is the one studied by Gornik in the context of matrix factorizations and the last one is new. Following an approach similar to Gornik’s we show that this new link homology can be described in terms of Khovanov’s original sl2–link homology.

DOI : 10.2140/agt.2007.7.1135
Keywords: $sl_3$, foams, Khovanov, link homology

Mackaay, Marco  1   ; Vaz, Pedro  1

1 Departamento de Matemática, Universidade do Algarve, Campus de Gambelas, 8005-139 Faro, Portugal 
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Mackaay, Marco; Vaz, Pedro. The universal sl3–link homology. Algebraic and Geometric Topology, Tome 7 (2007) no. 3, pp. 1135-1169. doi: 10.2140/agt.2007.7.1135

[1] D Bar-Natan, On Khovanov's categorification of the Jones polynomial, Algebr. Geom. Topol. 2 (2002) 337

[2] D Bar-Natan, Khovanov's homology for tangles and cobordisms, Geom. Topol. 9 (2005) 1443

[3] N M Dunfield, S Gukov, J Rasmussen, The superpolynomial for knot homologies, Experiment. Math. 15 (2006) 129

[4] B Gornik, Note on Khovanov link cohomology

[5] S Gukov, J Walcher, Matrix factorizations and Kauffman homology

[6] M Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000) 359

[7] M Khovanov, sl(3) link homology, Algebr. Geom. Topol. 4 (2004) 1045

[8] M Khovanov, Link homology and Frobenius extensions, Fund. Math. 190 (2006) 179

[9] M Khovanov, L Rozansky, Matrix factorizations and link homology

[10] G Kuperberg, Spiders for rank $2$ Lie algebras, Comm. Math. Phys. 180 (1996) 109

[11] E S Lee, An endomorphism of the Khovanov invariant, Adv. Math. 197 (2005) 554

[12] M Mackaay, P Turner, P Vaz, A remark on Rasmussen's invariant of knots, J. Knot Theory Ramifications 16 (2007) 333

[13] P R Turner, Calculating Bar-Natan's characteristic two Khovanov homology, J. Knot Theory Ramifications 15 (2006) 1335

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