  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.
