A compactness result for non-local unregularized gradient flow lines

TL;DR

This paper establishes a compactness theorem for non-local gradient flow lines in scale Hilbert spaces, advancing the mathematical foundation necessary for developing Floer theory in this context.

Contribution

It provides the first compactness result for non-local unregularized gradient flows on scale Hilbert spaces, enabling progress in Floer theory.

Findings

Proves an abstract compactness theorem for gradient flow lines.

Lays groundwork for Floer theory on scale Hilbert spaces.

First such result for non-local unregularized gradient flows.

Abstract

We prove an abstract compactness result for gradient flow lines of a non-local unregularized gradient flow equation on a scale Hilbert space. This is the first step towards Floer theory on scale Hilbert spaces.