Plane Floer homology and the odd Khovanov homology of 2-knots

TL;DR

This paper establishes a connection between plane Floer homology and odd Khovanov homology for 2-knots, proving a conjecture and aiming to develop a functorial model for the latter.

Contribution

It proves a conjecture relating odd Khovanov cobordism maps to plane Floer homology, introducing a new approach using Daemi's theory.

Findings

Confirmed the conjecture of Migdail and Wehrli.

Demonstrated the use of plane Floer homology as an alternative to Lee deformation.

Paved the way for a functorial model of odd Khovanov homology.

Abstract

We prove a conjecture of Migdail and Wehrli regarding the odd Khovanov cobordism maps associated to knotted spheres. Our key tool is Daemi's plane Floer homology, which we use in place of a Lee deformation. Continuing the analogy with Lee homology, we see this work as a potential first step toward a genuinely functorial model for odd Khovanov homology.