S. V. Buyalo, “Möbius and sub-Möbius structures”, Algebra i Analiz, 2016, Volume 28, Issue 5,Pages <nobr>1

This article is cited in 9 papers

Research Papers

Möbius and sub-Möbius structures

S. V. Buyalo

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

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.

Keywords: Möbius structure, cross-ratio, hyperbolic space.

Received: 05.08.2015