#### Volume 22, issue 5 (2018)

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Categorified Young symmetrizers and stable homology of torus links

### Matthew Hogancamp

Geometry & Topology 22 (2018) 2943–3002
##### Abstract

We show that the triply graded Khovanov–Rozansky homology of the torus link ${T}_{n,k}$ stabilizes as $k\to \infty$. We explicitly compute the stable homology, as a ring, which proves a conjecture of Gorsky, Oblomkov, Rasmussen and Shende. To accomplish this, we construct complexes ${P}_{n}$ of Soergel bimodules which categorify the Young symmetrizers corresponding to one-row partitions and show that ${P}_{n}$ is a stable limit of Rouquier complexes. A certain derived endomorphism ring of ${P}_{n}$ computes the aforementioned stable homology of torus links.

##### Mathematical Subject Classification 2010
Primary: 18G60, 57M27
##### Publication
Revised: 11 January 2018
Accepted: 13 February 2018
Published: 1 June 2018
Proposed: Ciprian Manolescu
Seconded: Jim Bryan, Haynes R Miller
##### Authors
 Matthew Hogancamp Department of Mathematics University of Southern California Los Angeles, CA United States