Generic jet evaluation transversality of contact instantons against contact distribution

TL;DR

This paper proves transversality results for contact instantons on coorientable contact manifolds, establishing generic properties of evaluation maps and jet transversality in the context of contact geometry.

Contribution

It introduces new transversality theorems for contact instantons, demonstrating genericity of certain evaluation maps and jet transversality conditions in contact geometry.

Findings

Proves interior and boundary evaluation maps are transverse for generic contact forms.

Establishes 1-jet transversality of contact instantons against contact distribution.

Provides foundational results for regularity and moduli space analysis in contact instanton theory.

Abstract

For a given coorientable contact manifold $(M,\Xi)$ with contact distribution $\Xi$, we consider its contact forms $\lambda$ with $\ker \lambda = \Xi$, and the associated contact triads $(M,\lambda, J)$. For a generic choice of contact form $\lambda$, we prove the (0-jet) the interior and boundary evaluation maps, and the 1-jet transversality of contact instantons (against contact distribution, for example).