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Möbius and sub-Möbius structures


Author: S. Buyalo
Translated by: the author
Original publication: Algebra i Analiz, tom 28 (2016), nomer 5.
Journal: St. Petersburg Math. J. 28 (2017), 555-568
MSC (2010): Primary 53C23
DOI: https://doi.org/10.1090/spmj/1463
Published electronically: July 25, 2017
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Abstract: The notion of a sub-Möbius structure is introduced, and necessary and sufficient conditions are found under which a sub-Möbius structure is a Möbius structure. It is shown that on the boundary at infinity $ \partial _{\infty } Y$ of every Gromov hyperbolic space $ Y$ there is a canonical sub-Möbius structure invariant under the isometries of $ Y$ and such that the sub-Möbius topology on $ \partial _{\infty } Y$ coincides with the standard one.


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Additional Information

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

DOI: https://doi.org/10.1090/spmj/1463
Keywords: M\"obius structures, cross-ratio, hyperbolic spaces
Received by editor(s): August 5, 2015
Published electronically: July 25, 2017
Additional Notes: Supported by RFBR (grant no. 14-01-00062)
Article copyright: © Copyright 2017 American Mathematical Society