Khovanov homology for virtual tangles and applications
Daniel Tubbenhauer
TL;DR
This paper extends the categorification of the virtual Jones polynomial to virtual tangles, providing a combinatorial, semi-local approach that enables new applications such as analyzing Lee's degeneration of virtual homology.
Contribution
It introduces a semi-local, combinatorial extension of Khovanov homology to virtual tangles, facilitating new applications in virtual knot theory.
Findings
Extended Khovanov homology to virtual tangles
Proved semi-local properties of the extension
Applied to Lee's degeneration of virtual homology
Abstract
We extend the cobordism based categorification of the virtual Jones polynomial to virtual tangles. This extension is combinatorial and has semi-local properties. We use the semi-local property to prove an applications, i.e. we give a discussion of Lee's degeneration of virtual homology.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology