Instantons and annular Khovanov homology

In this paper, we introduce the annular instanton Floer homology which is defined for links in a thickened annulus. It is an analogue of the annular Khovanov homology. A spectral sequence whose second page is the annular Khovanov homology and which converges to the annular instanton Floer homology is constructed. As an application of this spectral sequence, we prove that the annular Khovanov homology detects the unlink in the thickened annulus (assuming all the components are null-homologous). Another application is a new proof of Grigsby and Ni's result that tangle Khovanov homology distinguishes braids from other tangles. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper introduces the annular instanton Floer homology and constructs a spectral sequence for links in a thickened annulus, with applications in detecting the unlink and distinguishing braids from other tangles using the annular Khovanov homology.