Embedding-Projection Correspondences for the estimation of the Gromov-Hausdorff distance

TL;DR

This paper explores a novel method called embedding-projection correspondences (EPCs) for estimating the Gromov-Hausdorff distance between compact metric spaces, focusing on spheres of varying dimensions.

Contribution

It introduces EPCs as a new approach to compare metric spaces and investigates their properties, especially for spheres of different dimensions.

Findings

EPCs provide a new framework for estimating Gromov-Hausdorff distances.

Initial results show promising applications for comparing spheres of different dimensions.

Further testing and analysis are ongoing.

Abstract

This writeup describes ongoing work on designing and testing a certain family of correspondences between compact metric spaces that we call \emph{embedding-projection correspondences} (EPCs). Of particular interest are EPCs between spheres of different dimension.