Complexity of distances: Reductions of distances between metric and Banach spaces
Abstract
We show that all the standard distances from metric geometry and functional analysis, such as Gromov-Hausdorff distance, Banach-Mazur distance, Kadets distance, Lipschitz distance, Net distance, and Hausdorff-Lipschitz distance have all the same complexity and are reducible to each other in a precisely defined way. This is done in terms of descriptive set theory and is a part of a larger research program initiated by the authors in \emph{Complexity of distances: Theory of generalized analytic equivalence relations}. The paper is however targeted also to specialists in metric geometry and geometry of Banach spaces.
Keywords
Cite
@article{arxiv.2004.11752,
title = {Complexity of distances: Reductions of distances between metric and Banach spaces},
author = {Marek Cúth and Michal Doucha and Ondřej Kurka},
journal= {arXiv preprint arXiv:2004.11752},
year = {2022}
}
Comments
Accepted in Israel Journal of Mathematics. This paper is a result of splitting the original arxiv submission arXiv:1804.11164 into two parts and some polishing. This is the second part. The original submission arXiv:1804.11164 has been replaced by the first part of the split