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 an analogue of Khovanov homology. A spectral sequence whose second page and converges to constructed. As application sequence, prove that detects unlink annulus (assuming all components are null-homologous). Another new proof Grigsby Ni's result tangle distinguishes braids from other tangles.