On the manifold structure of the set of unparameterized embeddings with low regularity

TL;DR

This paper investigates the geometric structure of the space of low-regularity embeddings of a compact manifold into another manifold, considering the quotient by diffeomorphisms, to understand their manifold properties.

Contribution

It provides a detailed analysis of the manifold structure of unparameterized embeddings with low regularity, extending classical smooth embedding theory.

Findings

Characterization of the manifold structure for low-regularity embeddings

Identification of the quotient space by diffeomorphisms as a geometric object

Extension of smooth embedding concepts to less regular contexts

Abstract

Given manifolds $M$ and $N$, with $M$ compact, we study the geometrical structure of the space of embeddings of $M$ into $N$, having less regularity than $\mathcal C^\infty$, quotiented by the group of diffeomorphisms of $M$.