Floerfolds and Floer functions

TL;DR

This paper introduces Floer functions and Floerfolds, establishing an intrinsic framework for Floer functions with Hessians as Fredholm operators of index zero, despite their complex transformation properties.

Contribution

The paper defines Floerfolds to make the concept of Floer functions intrinsic, overcoming transformation issues of the Hessian in Floer theory.

Findings

Floer functions have Hessians that are Fredholm operators of index zero.

Floerfolds provide an intrinsic setting for Floer functions.

The notion of Floer functions is made independent of chart transitions.

Abstract

In this article we introduce the notion of Floer function which has the property that the Hessian is a Fredholm operator of index zero in a scale of Hilbert spaces. Since the Hessian has a complicated transformation under chart transition, in general this is not an intrinsic condition. Therefore we introduce the concept of Floerfolds for which we show that the notion of Floer function is intrinsic.