Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
35/2019

Topology and curvature of metric spaces

Parvaneh Joharinad and Jürgen Jost

Abstract

We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Busemann, our concept also applies to metric spaces that might be discrete. The natural comparison spaces that emerge from our discussion are no longer Euclidean spaces, but rather tripod spaces. These tripod spaces include the hyperconvex spaces which have trivial Čech homology. This suggests a link of our geometrical method to the topological method of persistent homology employed in topological data analysis. We also investigate the geometry of general tripod spaces.

Received:
Apr 1, 2019
Published:
Apr 1, 2019
Keywords:
Curvature inequality, discrete metric space, hyperconvex, hyperbolic, intersection of balls, tripod

Related publications

inJournal
2019 Repository Open Access
Parvaneh Joharinad and Jürgen Jost

Topology and curvature of metric spaces

In: Advances in mathematics, 356 (2019), p. 106813