14 citations · 27 across the 6 of their papers we have counts for
13 papers · 1 filter
Hopfological algebra and categorification at a root of unity: the first steps
Mikhail Khovanov
Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories ov…
Link homology and Frobenius extensions
Mikhail Khovanov
We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan theories, equivariant cohom…
Matrix factorizations and link homology
Mikhail Khovanov, Lev Rozansky
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…
Homological realization of Nakajima varieties and Weyl group actions
Igor Frenkel, Mikhail Khovanov, Olivier Schiffmann
We describe points on Nakajima varieties and Weyl group actions on them via complexes of semisimple and projective modules over certain finite-dimensional algebras.
Categorifications of the colored Jones polynomial
Mikhail Khovanov
The colored Jones polynomial of links has two natural normalizations: one in which the n-colored unknot evaluates to [n+1], the quantum dimension of the (n+1)-dimensional irreducib…
An invariant of tangle cobordisms
Mikhail Khovanov
We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.