A contact homotopy type

TL;DR

This paper develops a new framework for contact homology by constructing flow categories from Reeb orbits and pseudo-holomorphic buildings, extending the theory to cobordisms and providing a natural, functorial approach.

Contribution

It introduces a contact homotopy type via flow categories and bimodules, adapting Kuranishi chart techniques to the contact setting for the first time.

Findings

Constructs flow categories from Reeb orbits and pseudo-holomorphic buildings.

Lifts contact homology to a functorial setting with cobordisms.

Provides a natural, geometric framework for contact homology.

Abstract

Adapting the construction of global Kuranishi charts to the contact setting, we associate to any non-degenerate contact manifold a flow category based on Reeb orbits and moduli spaces of pseudo-holomorphic buildings. The construction lifts contact homology and is natural in the sense that to any exact symplectic cobordism we can associate a flow bimodule between the flow categories of its ends.