Annular Khovanov homology and augmented links

Abstract

Given an annular link $L$, there is a corresponding augmented link $\tilde{L}$ in $S^3$ obtained by adding a meridian unknot component to $L$. In this paper, we construct a spectral sequence with the second page isomorphic to the annular Khovanov homology of $L$ and it converges to the reduced Khovanov homology of $\tilde{L}$. As an application, we classify all the links with the minimal rank of annular Khovanov homology. We also give a proof that annular Khovanov homology detects unlinks.

12 pages, 10 figures

References in corpus (5)

• Khovanov's homology for tangles and cobordisms
• Matrix factorizations and link homology II
• Categorification of the Kauffman bracket skein module of I-bundles over surfaces
• On knot Floer homology in double branched covers
• Instanton Floer homology for sutured manifolds with tangles