Categorified Young symmetrizers and stable homology of torus links

Hogancamp, Matthew¹

¹ Department of Mathematics, University of Southern California, Los Angeles, CA, United States

Geometry & topology, Tome 22 (2018) no. 5, pp. 2943-3002

Résumé

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.

Détail

DOI : 10.2140/gt.2018.22.2943

Classification : 18G60, 57M27
Keywords: link homology, categorification

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