Khovanov homology for links in thickened multipunctured disks

TL;DR

This paper introduces a new variant of Khovanov homology for links in thickened disks with multiple punctures, establishing relations to existing theories through spectral sequences and surface embeddings.

Contribution

It defines a novel Khovanov homology variant for punctured disks and connects it to prior work via spectral sequences and surface embedding-induced spectral sequences.

Findings

New Khovanov homology variant for punctured disks

Spectral sequences relate the new theory to existing homologies

Embeddings induce spectral sequences recovering known results

Abstract

We define a variant of Khovanov homology for links in thickened disks with multiple punctures. This theory is distinct from the one previously defined by Asaeda, Przytycki, and Sikora, but is related to it by a spectral sequence. Additionally, we show that there are spectral sequences induced by embeddings of thickened surfaces, which recover the spectral sequence from annular Khovanov homology to Khovanov homology as a special case.