On Gradings in Khovanov homology and sutured Floer homology
J. Elisenda Grigsby, Stephan M. Wehrli
TL;DR
This paper explores the relationship between gradings in Khovanov homology and sutured Floer homology, providing explicit connections and interpretations within spectral sequences.
Contribution
It introduces a detailed analysis of the gradings in both theories and clarifies their representation-theoretic and geometric interpretations.
Findings
Explicit relationship between Z and 1/2 Z gradings established
Representation-theoretic and geometric interpretations clarified
Generalizations of Ozsvath-Szabo's spectral sequence discussed
Abstract
We discuss generalizations of Ozsvath-Szabo's spectral sequence relating Khovanov homology and Heegaard Floer homology, focusing attention on an explicit relationship between natural Z (resp., 1/2 Z) gradings appearing in the two theories. These two gradings have simple representation-theoretic (resp., geometric) interpretations, which we also review.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Numerical Analysis Techniques · Homotopy and Cohomology in Algebraic Topology