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St. Petersburg Mathematical Journal

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Ptolemy spaces with strong inversions

Author: A. Smirnov
Translated by: the author
Original publication: Algebra i Analiz, tom 25 (2013), nomer 6.
Journal: St. Petersburg Math. J. 25 (2014), 1021-1030
MSC (2010): Primary 53C70
Published electronically: September 8, 2014
MathSciNet review: 3234843
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Abstract: It is proved that a compact Ptolemy space with many strong inversions that contains a Ptolemy circle is Möbius equivalent to an extended Euclidean space.

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Additional Information

A. Smirnov
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, Saint Petersburg 191023, Russia

Keywords: Ptolemy space, M\"obius structure
Received by editor(s): January 23, 2013
Published electronically: September 8, 2014
Additional Notes: Supported by RFBR (grant no. 11-01-00302-a).
Article copyright: © Copyright 2014 American Mathematical Society