An oriented model for Khovanov homology

By C. Blanchet. 2010

70 citations recorded by the source corpus.

We give an alternative presentation of Khovanov homology of links with strict functoriality result over integers. The construction uses an oriented $sl(2)$ state model allowing a natural definition of the boundary operator as twisted action of morphisms belonging to a TQFT for trivalent graphs and surfaces.

View Paper: https://www.semanticscholar.org/paper/95d8b060105eb806d6805f9b14d25b5c9e63ad37

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Citations in the corpus

The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality (2014, methodology): “Acknowledgements: We’d like to thank Christian Blanchet, Sabin Cautis, Ben Cooper, Matt Hogancamp, Mikhail Khovanov, Tony Licata, Scott Morrison, Lev Rozansky, and Hao Wu for helpful discussions, and Daniel Tubbenhauer for his careful reading of a preliminary draft of this paper.”
Functoriality of colored link homologies (2017, methodology): “r link cobordisms. This result is new to the best of our knowledge, except in low-rank cases. For N= 2, functorial theories were obtained by Caprau [Cap08], Clark{Morrison{Walker [CMW09] and Blanchet [Bla10] after Khovanov’s original theory turned out to have a sign ambiguity, see Jacobsson [Jac04] ”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “These relations are similar to the ones of [53] in the sl3 case, but in the sl2 case we obtain relations that slightly extend both Blanchet’s [4] and Clark-Morrison-Walker [21] models.”
Quantum link homology via trace functor I (2016, methodology): “category. This was done successfully for F= R2 by Clark, Morrison and Walker using cobordisms with seams and coeﬃcients in the ring ofGaussian integers Z[i] [CMW09], then by Blanchet using nodalfoams [Bla10] and by Vogel using mixed cobordisms: locally oriented cobordisms with certain disorientation”