sl(3) link homology

By Mikhail Khovanov. 2003

231 citations recorded by the source corpus.

Author(s): Khovanov, Mikhail | Abstract: We define a bigraded homology theory whose Euler characteristic is the quantum sl(3) link invariant.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d48bc2d42c1abc152e32b8a1b0bab6be5e3a8801

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Khovanov homology is a skew Howe 2-representation of categorified quantum sl(m) (2012, methodology): “When n = 3, the latter of these link homologies can then be identified [56] with Khovanov’s more elementary construction [32] of sl3 link homology defined using singular cobordisms called foams.”
Webs and quantum skew Howe duality (2012, background): “Khovanov homology is a skew Howe 2-representation of categorified quantum slm. arXiv:1212.6076.”
The $\mathfrak{sl}_n$ foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality (2014, methodology): “Khovanov himself gave a construction of sl3 link homology in the spirit of the invariant mentioned above [23], and, in joint work with Rozansky, later gave a construction based on the theory of matrix factorizations [30] which generalizes both of the above approaches to sln for all n ≥ 2.”
sl.N/-link homology (N 4) using foams and the Kapustin-Li formula (2007, methodology): “In this paper we use foams, as in [1; 7; 12], for an almost completely combinatorial topological construction of a rational link homology categorifying the sl.”
A diagrammatic category for the representation theory of ( Uqsln ) (2007, background): “Khovanov’s work [18] on a foam model for sl3 link homology categorifies the Uq(sl3) theory, although it’s only made explicitly local in later work by Ari Nieh and myself [25].”
The universal sl3–link homology (2006, methodology): “In figure 5 we also have a set of useful identities which establish the way we can exchange dots between faces.”
Man and machine thinking about the smooth 4-dimensional Poincaré conjecture (2009, background): “Khovanov homology (or its variants categorifying the sl3 polynomial [27], [33], [35] or sln polynomials [29], [30], [43]) may hold promise for establishing that a link L is not slice.”
Functoriality of colored link homologies (2017, methodology): “Foams were first used by Khovanov for the definition of an sl3 homology [23].”
A combinatorial approach to functorial quantum slk knot invariants (2007, methodology): “Conjecturally our setup actually gives the representation theoretical background for the very recent generalisation [19] of [16] to arbitrary k.”
Note on Khovanov link cohomology (2004, background): “This algebra is the analogue of R(Γ) introduced in [5], section 6.”
Tait colorings, and an instanton homology for webs and foams (2015, methodology): “The proof mirrors Khovanov’s argument in [7].”
Fivebranes and 3-manifold homology (2016, background): “2)? The answer to these questions came a bit later, with the advent of the HOMFLYPT knot homology and its “colored” variants, which came as a surprise [8].”