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math.MG2012
Ptolemy spaces with strong inversions
Alexander Smirnov
We prove that a compact Ptolemy space with many strong inversions that contains a Ptolemy circle is Moebius equivalent to an extended Euclidean space.
math.GT2012
Quasi-isometric embedding of the fundamental group of an orthogonal graph-manifold into a product of metric trees
Alexander Smirnov
In every dimension we introduce a class of orthogonal graph-manifolds and prove that the fundamental group of any orthogonal graph-manifold quasi-isometrically embeds into…