Volume 22, issue 5 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23, 1 issue

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Other MSP Journals
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 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.

Keywords
link homology, categorification
Mathematical Subject Classification 2010
Primary: 18G60, 57M27
References
Publication
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
Authors
Matthew Hogancamp
Department of Mathematics
University of Southern California
Los Angeles, CA
United States