Geodesic
Möbius structures, quasimetrics and completeness
Incerti-Medici, Merlin1
1 Fakultät für Mathematik, Karlsruher Institut für Technologie, Karlsruhe, Germany
Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 1809-1840

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2024.24.1809
Keywords: cross ratio, quasimetrics, topology

Incerti-Medici, Merlin 1

1 Fakultät für Mathematik, Karlsruher Institut für Technologie, Karlsruhe, Germany 
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Incerti-Medici, Merlin. Möbius structures, quasimetrics and completeness. Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 1809-1840. doi: 10.2140/agt.2024.24.1809

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