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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Möbius structures and timed causal spaces on the circle


Author: S. Buyalo
Translated by: THE AUTHOR
Original publication: Algebra i Analiz, tom 29 (2017), nomer 5.
Journal: St. Petersburg Math. J. 29 (2018), 715-747
MSC (2010): Primary 51B10, 53C50
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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Additional Information

S. Buyalo
Affiliation: St. Petersburg Branch, Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: sbuyalo@pdmi.ras.ru

DOI: https://doi.org/10.1090/spmj/1513
Keywords: M\"obius structures, cross-ratio, harmonic 4-tuple, hyperbolic spaces, spacetimes, de Sitter space
Received by editor(s): May 5, 2016
Published electronically: July 26, 2018
Additional Notes: Supported by RFBR (grant no. 17-01-00128a)
Article copyright: © Copyright 2018 American Mathematical Society

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