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Möbius structures, quasimetrics and completeness

Merlin Incerti-Medici

Algebraic & Geometric Topology 24 (2024) 1809–1840
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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