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Categorified Young symmetrizers and stable homology of torus links

Matthew Hogancamp

Geometry & Topology 22 (2018) 2943–3002

We show that the triply graded Khovanov–Rozansky homology of the torus link Tn,k stabilizes as k . 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 Pn of Soergel bimodules which categorify the Young symmetrizers corresponding to one-row partitions and show that Pn is a stable limit of Rouquier complexes. A certain derived endomorphism ring of Pn computes the aforementioned stable homology of torus links.

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link homology, categorification
Mathematical Subject Classification 2010
Primary: 18G60, 57M27
Received: 16 March 2017
Revised: 11 January 2018
Accepted: 13 February 2018
Published: 1 June 2018
Proposed: Ciprian Manolescu
Seconded: Jim Bryan, Haynes R Miller
Matthew Hogancamp
Department of Mathematics
University of Southern California
Los Angeles, CA
United States