Smooth structure on the moduli space of instantons of a generic vector field

TL;DR

This paper explores the geometric structure of the space of instantons and unstable manifolds for a generic smooth vector field, revealing a smooth manifold with corners structure.

Contribution

It establishes a detailed description of the smooth manifold with corners structure on the space of broken instantons and unstable manifolds for generic vector fields.

Findings

The space of broken instantons forms a smooth manifold with corners.

The completion of unstable manifolds also admits a smooth manifold with corners structure.

The results are formalized in Theorem 1.4.

Abstract

This paper is a short version of some joint work with Stefan Haller. It describes the structure of "smooth manifold with corners" on the space of possibly broken instantons and on the completion of unstable manifolds of a generic smooth vector field. The result is stated in Theorem 1.4.