Chain homotopy maps and a universal differential for Khovanov-type homology
Noboru Ito
TL;DR
This paper introduces chain homotopy maps for a universal differential in Khovanov-type homology, unifying various differentials and ensuring Reidemeister invariance, advancing the theoretical framework of link homology.
Contribution
It provides explicit chain homotopy maps for the universal differential in Khovanov-type homology and analyzes conditions for Reidemeister invariance.
Findings
Constructed chain homotopy maps for the universal differential.
Identified conditions for Reidemeister invariance.
Unified original and Lee's differentials within a universal framework.
Abstract
We give chain homotopy maps of Khovanov-type link homology of a universal differential. The universal differential, discussed by Mikhail Khovanov, Marco Mackaay, Paul Turner and Pedro Vaz, contains the original Khovanov's differential and Lee's differential. We also consider the conditions of any differential ensuring the Reidemeister invariance for the chain homotopy maps.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis