Möbius structures and timed causal spaces on the circle

Buyalo, S.

doi:10.1090/spmj/1513

Möbius structures and timed causal spaces on the circle
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by S. Buyalo
Translated by: THE AUTHOR

St. Petersburg Math. J. 29 (2018), 715-747

DOI: https://doi.org/10.1090/spmj/1513

Published electronically: July 26, 2018

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Abstract:

A conjectural duality is discussed between hyperbolic spaces on one hand and spacetimes on the other, living on the opposite sides of the common absolute. This duality goes via Möbius structures on the absolute, and it is easily recognized in the classical case of symmetric rank one spaces. In the general case, no trace of such duality is known. As a first step in this direction, it is shown how numerous Möbius structures on the circle, including those that stem from hyperbolic spaces, give rise to 2-dimensional spacetimes, which are axiomatic versions of de Sitter 2-space, and vice versa. The paper has two Appendices, one of which is written by V. Schroeder.

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