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Matrix factorizations and link homology
Author(s): Khovanov, Mikhail; Rozansky, Lev | Abstract: For each positive integer n the HOMFLY polynomial of links specializes to a one-variable polynomial that can be recovered from the
A categorification of the Jones polynomial
Author(s): Khovanov, Mikhail | Abstract: We construct a bigraded cohomology theory of links whose Euler characteristic is the Jones polynomial.
A functor-valued invariant of tangles
We construct a family of rings. To a plane diagram of a tangle we associate a complex of bimodules over these rings. Chain homotopy equivalence class of this complex is an invariant of the tangle. On
Link homology and Frobenius extensions
Author(s): Khovanov, Mikhail | Abstract: We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan
Triply-graded link homology and Hochschild homology of Soergel bimodules
We consider a class of bimodules over polynomial algebras which were originally introduced by Soergel in relation to the Kazhdan–Lusztig theory, and which describe a direct summand of the category of
sl(3) link homology
Author(s): Khovanov, Mikhail | Abstract: We define a bigraded homology theory whose Euler characteristic is the quantum sl(3) link invariant.
Matrix factorizations and link homology II
For each positive integer n the HOMFLY polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a
Heisenberg algebra and a graphical calculus
A new calculus of planar diagrams involving diagrammatics for biadjoint functors and degenerate affine Hecke algebras is introduced. The calculus leads to an additive monoidal category whose
Web bases for sl(3) are not dual canonical
We compare two natural bases for the invariant space of a tensor product of irreducible representations of A_2, or sl(3). One basis is the web basis, defined from a skein theory called the
Quivers, Floer cohomology, and braid group actions
We consider the derived categories of modules over a certain family A_m of graded rings, and Floer cohomology of Lagrangian intersections in the symplectic manifolds which are the Milnor fibres of
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