A type D structure in Khovanov homology
Lawrence P. Roberts
TL;DR
This paper introduces a new combinatorial approach to associating a type D structure to tangles in Khovanov homology, establishing its invariance and laying groundwork for a gluing theory.
Contribution
It develops the first part of a gluing theory for bigraded Khovanov homology using combinatorial methods, linking it to bordered Heegaard-Floer homology.
Findings
Type D structure is an invariant of tangle isotopy.
Constructs a combinatorial model for Khovanov homology.
Lays foundation for a gluing theory in Khovanov homology.
Abstract
We describe the first part of a gluing theory for the bigraded Khovanov homology with integer coefficients. This part associates a type D structure to a tangle properly embedded in a half-space and proves that the homotopy class of the type D structure is an invariant of the isotopy class of the tangle. The construction is modeled off bordered Heegaard-Floer homology, but uses only combinatorial/diagrammatic methods
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis