Khovanov homology for links in thickened multipunctured disks (Q6614443)

The paper introduces a variant of Khovanov homology for links in thickened disks with multiple punctures. By presenting this new variant, the author broadens the applicability of Khovanov homology and also demonstrates its relation to the theory previously defined by Asaeda, Przytycki, and Sikora [\textit{M. M. Asaeda} et al., Algebr. Geom. Topol. 4, 1177--1210 (2004; Zbl 1070.57008)] through a spectral sequence. This connection serves as a bridge for future research, potentially fostering interdisciplinary applications between different theoretical frameworks. The paper also discusses the potential uses of the new theory in distinguishing types of knots and extracting information about braids. These applications are expected to have a positive impact on the theoretical classification and practical applications of knots.