Volume 18, issue 2 (2018)

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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