Möbius structures, quasimetrics and completeness

Incerti-Medici, Merlin

doi:10.2140/agt.2024.24.1809

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Möbius structures, quasimetrics and completeness

Merlin Incerti-Medici

Algebraic & Geometric Topology 24 (2024) 1809–1840

DOI: 10.2140/agt.2024.24.1809

Abstract

We study cross ratios from an axiomatic viewpoint, also known as the study of Möbius spaces. We characterise cross ratios induced by quasimetrics in terms of topological properties of their image. Furthermore, we generalise the notions of Cauchy sequences and completeness to Möbius spaces and prove the existence of a unique completion under an extra assumption that, again, can be expressed in terms of the image of the cross ratio.

Keywords

cross ratio, quasimetrics, topology

Mathematical Subject Classification

Primary: 20F65

Secondary: 53C23

References

Publication

Received: 5 May 2020

Revised: 20 November 2021

Accepted: 2 March 2023

Published: 16 July 2024

Authors

Merlin Incerti-Medici
Fakultät für Mathematik Karlsruher Institut für Technologie Karlsruhe Germany

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Volume 24, issue 4 (2024)