Embedded contact homology of the unit cotangent bundle of the Klein bottle

TL;DR

This paper provides a combinatorial description of the embedded contact homology of the unit cotangent bundle of the Klein bottle, leading to new results on symplectic embeddings and the Gromov width.

Contribution

It introduces a combinatorial approach to embedded contact homology for the Klein bottle's cotangent bundle and applies it to symplectic embedding obstructions and width calculations.

Findings

Obstruction theorem for symplectic embeddings of toric domains into the Klein bottle's cotangent bundle

Explicit computation of the Gromov width of the unit cotangent bundle of the Klein bottle

Development of a combinatorial description of embedded contact homology for this setting

Abstract

We give a combinatorial description of the embedded contact homology chain complex of the unit cotangent bundle of the Klein bottle with the standard flat Riemannian metric. Using pseudoholomorphic curves coming from the associated differential, we find an obstruction theorem for symplectic embeddings of toric domains $X_\Omega \subset \mathbb{C}^2$ into the unit disk cotangent bundle $D^*K$. As an application we compute the Gromov width of $D^*K$.