sl.N/-link homology (N 4) using foams and the Kapustin-Li formula

By Marco Mackaay, Marko Stosic, Pedro Vaz. 2007

102 citations recorded by the source corpus.

We use foams to give a topological construction of a rational link homology categorifying the slN link invariant, for N>3. To evaluate closed foams we use the Kapustin-Li formula adapted to foams by Khovanov and Rozansky. We show that for any link our homology is isomorphic to Khovanov and Rozansky's.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0d313529f60d8ec4bd92a9b735c20d5ecbc64325

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In Computational Theory and Mathematics

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Citations in the corpus

An oriented model for Khovanov homology (2010, methodology): “Our construction can be understood as N = 2 special case of sl(N) link homology first constructed by Khovanov–Rozansky [13] with matrix factorizations and obtained via foams by McKaay–Stosic–Vaz [18].”
Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “For general sln, matrix factorizations become the primary computation tool [77, 76, 75], and the only way to evaluate a closed foam is through the mysterious Kapustin-Li formula [51, 23].”
Tait colorings, and an instanton homology for webs and foams (2015, background): “(Singular points of this type appear in the foams of [17].”
Knot invariants and higher representation theory II: the categorification of quantum knot invariants (2010, result): “tion for all n (this is conjectured in [MS09]), but actually proving this requires an improvement in the state of understanding of the relationship between the foam model of Mackaay, Stosˇi´c and Vaz [MSV09] and 36 Ben Webster the model we have presented. It would also be desirable to compare our re”