Volume 18, issue 2 (2018)

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

Volume 24
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
A rank inequality for the annular Khovanov homology of $2\mskip-1.5mu$–periodic links

Melissa Zhang

Algebraic & Geometric Topology 18 (2018) 1147–1194
Abstract

For a 2–periodic link L̃ in the thickened annulus and its quotient link L, we exhibit a spectral sequence with

E1AKh(L̃) FF[θ,θ1] EAKh(L) FF[θ,θ1].

This spectral sequence splits along quantum and sl2 weight-space gradings, proving a rank inequality rkAKhj,k(L) rkAKh2jk,k(L̃) for every pair of quantum and sl2 weight-space gradings (j,k). We also present a few decategorified consequences and discuss partial results toward a similar statement for the Khovanov homology of 2–periodic links, as well as some frameworks for obstructing 2–periodicity in links.

Keywords
Khovanov homology, periodic links, localization
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57M60
References
Publication
Received: 14 July 2017
Revised: 2 November 2017
Accepted: 25 November 2017
Published: 12 March 2018
Authors
Melissa Zhang
Department of Mathematics
Boston College
Chestnut Hill, MA
United States