Algebraic & Geometric Topology

A rank inequality for the annular Khovanov homology of $2$–periodic links

Melissa Zhang

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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.

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 2 (2018), 1147-1194.

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1521684033

Digital Object Identifier
doi:10.2140/agt.2018.18.1147

Mathematical Reviews number (MathSciNet)
MR3773751

Zentralblatt MATH identifier
06859617

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds
Secondary: 57M60: Group actions in low dimensions

Keywords
Khovanov homology periodic links localization

Citation

Zhang, Melissa. A rank inequality for the annular Khovanov homology of $2$–periodic links. Algebr. Geom. Topol. 18 (2018), no. 2, 1147--1194. doi:10.2140/agt.2018.18.1147. https://projecteuclid.org/euclid.agt/1521684033


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