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2018 A rank inequality for the annular Khovanov homology of $2$–periodic links
Melissa Zhang
Algebr. Geom. Topol. 18(2): 1147-1194 (2018). DOI: 10.2140/agt.2018.18.1147

Abstract

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

E 1 AKh ( L ̃ ) F F [ θ , θ 1 ] E AKh ( L ) F F [ θ , θ 1 ] .

This spectral sequence splits along quantum and s l 2 weight-space gradings, proving a rank inequality rk AKh j , k ( L ) rk AKh 2 j k , k ( L ̃ ) for every pair of quantum and s l 2 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.

Citation

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Melissa Zhang. "A rank inequality for the annular Khovanov homology of $2$–periodic links." Algebr. Geom. Topol. 18 (2) 1147 - 1194, 2018. https://doi.org/10.2140/agt.2018.18.1147

Information

Received: 14 July 2017; Revised: 2 November 2017; Accepted: 25 November 2017; Published: 2018
First available in Project Euclid: 22 March 2018

zbMATH: 06859617
MathSciNet: MR3773751
Digital Object Identifier: 10.2140/agt.2018.18.1147

Subjects:
Primary: 57M25, 57M27
Secondary: 57M60

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 2 • 2018
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