Notes on Matrix Factorizations and Knot Homology

@article{Oblomkov2019NotesOM,
  title={Notes on Matrix Factorizations and Knot Homology},
  author={Alexei Oblomkov},
  journal={Lecture Notes in Mathematics},
  year={2019}
}
  • A. Oblomkov
  • Published 13 January 2019
  • Mathematics
  • Lecture Notes in Mathematics
These are the notes of the lectures delivered by the author at CIME in June 2018. The main purpose of the notes is to provide an overview of the techniques used in the construction of the triply graded link homology. The homology is the space of global sections of a particular sheaf on the Hilbert scheme of points on the plane. Our construction relies on existence on the natural push-forward functor for the equivariant matrix factorizations, we explain the subtleties on the construction in… Expand
HOMFLY POLYNOMIALS FROM THE HILBERT SCHEMES OF A PLANAR CURVE,
Among the most interesting invariants one can associate with an oriented link L ⊂ S3 is its homfly-pt polynomial P(L, v, s) ∈ Z[v±1, (s − s−1)±1] ([13, 33]). In 2010 A. Oblomkov and V. Shende ([32])Expand
A G ] 2 3 A ug 2 02 1 Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School
3 Khovanov-Rozansky homology: definitions and computations 6 3.1 Soergel bimodules and Rouquier complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2 Khovanov-Rozansky homology . . .Expand

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