Deformations and transversality of pseudo-holomorphic discs

TL;DR

This paper establishes foundational theorems for pseudo-holomorphic discs, demonstrating their transversality properties and manifold structure, which are crucial for understanding their geometric and topological behavior.

Contribution

It introduces analogs of classical theorems for pseudo-holomorphic discs, showing they form a manifold and possess transversality properties.

Findings

Pseudo-holomorphic discs satisfy analogs of Thom's transversality theorem.

Pseudo-holomorphic discs form a smooth manifold.

The results extend classical differential topology to the setting of pseudo-holomorphic curves.

Abstract

We prove analogs of Thom's transversality theorem and Whitney's theorem on immersions for pseudo-holomorphic discs. We also prove that pseudo-holomorphic discs form a manifold.