#### Volume 18, issue 2 (2018)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 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 $2\phantom{\rule{0.3em}{0ex}}$–periodic link $\stackrel{̃}{L}$ in the thickened annulus and its quotient link $L$, we exhibit a spectral sequence with

${E}^{1}\cong AKh\left(\stackrel{̃}{L}\right){\otimes }_{\mathbb{F}}\mathbb{F}\left[\theta ,{\theta }^{-1}\right]⇉{E}^{\infty }\cong AKh\left(L\right){\otimes }_{\mathbb{F}}\mathbb{F}\left[\theta ,{\theta }^{-1}\right].$

This spectral sequence splits along quantum and ${\mathfrak{s}\mathfrak{l}}_{2}$ weight-space gradings, proving a rank inequality $rk{AKh}^{j,k}\left(L\right)\le rk{AKh}^{2j-k,k}\left(\stackrel{̃}{L}\right)$ for every pair of quantum and ${\mathfrak{s}\mathfrak{l}}_{2}$ weight-space gradings $\left(j,k\right)$. We also present a few decategorified consequences and discuss partial results toward a similar statement for the Khovanov homology of $2\phantom{\rule{0.3em}{0ex}}$–periodic links, as well as some frameworks for obstructing $2\phantom{\rule{0.3em}{0ex}}$–periodicity in links.

##### Keywords
Khovanov homology, periodic links, localization
##### Mathematical Subject Classification 2010
Primary: 57M25, 57M27
Secondary: 57M60
##### 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