On the computation of torus link homology

We introduce a new method for computing triply graded link homology, which is particularly well adapted to torus links. Our main application is to the $(n,n)$ -torus links, for which we give an exact answer for all $n$ . In several cases, our computations verify conjectures of Gorsky et al. relating homology of torus links with Hilbert schemes.

[1]  Stable homology of torus links via categorified Young symmetrizers I: one-row partitions , 2015 .

[2]  Evgeny Gorsky,et al.  On Stable Khovanov Homology of Torus Knots , 2012, Exp. Math..

[3]  Eugene Gorsky,et al.  Refined knot invariants and Hilbert schemes , 2013, 1304.3328.

[4]  Ben Elias,et al.  The Hodge theory of Soergel bimodules , 2012, 1212.0791.

[5]  Categorification of the braid groups , 2004, math/0409593.

[6]  Ben Elias,et al.  Categorical Diagonalization , 2017, Introduction to Soergel Bimodules.

[7]  Alexei Oblomkov,et al.  Torus knots and the rational DAHA , 2012, 1207.4523.

[8]  KAZHDAN-LUSZTIG-POLYNOME UND UNZERLEGBARE BIMODULN ÜBER POLYNOMRINGEN , 2006, Journal of the Institute of Mathematics of Jussieu.

[9]  Elisabetta Strickland,et al.  Lectures on quasi-invariants of Coxeter groups and the Cherednik algebra , 2002 .

[10]  Categorical diagonalization of full twists , 2017, 1801.00191.

[11]  Matthew Hogancamp,et al.  Categorified Young symmetrizers and stable homology of torus links II , 2015, Selecta Mathematica.

[12]  Mikhail Khovanov,et al.  Triply-graded link homology and Hochschild homology of Soergel bimodules , 2005, math/0510265.

[13]  Matthew Hogancamp.  Khovanov-Rozansky homology and higher Catalan sequences , 2017, 1704.01562.

[14]  E. Gorsky.  q,t-Catalan numbers and knot homology , 2010, 1003.0916.

[15]  Mikhail Khovanov,et al.  Matrix factorizations and link homology , 2008 .

[16]  Gorsky Evgeny,et al.  Flag Hilbert schemes, colored projectors and Khovanov-Rozansky homology , 2016 .

[17]  Jacob Rasmussen,et al.  Some differentials on Khovanov–Rozansky homology , 2006, math/0607544.

[18]  M. Khovanov,et al.  Braid cobordisms, triangulated categories, and flag varieties , 2006, math/0609335.

[19]  The Annular Structure of Subfactors , 2001, math/0105071.

[20]  Daniel Krasner,et al.  Rouquier Complexes are Functorial over Braid Cobordisms , 2009, 0906.4761.

[21]  Benita Elias,et al.  Soergel Calculus , 2013, 1309.0865.