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Quasiisometric embedding of the fundamental group of an orthogonal graph-manifold into a product of metric trees

Author: A. Smirnov
Translated by: the author
Original publication: Algebra i Analiz, tom 24 (2012), nomer 5.
Journal: St. Petersburg Math. J. 24 (2013), 811-821
MSC (2010): Primary 57M15
Published electronically: July 24, 2013
MathSciNet review: 3087825
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Abstract: In every dimension $ n\ge 3$, a class of orthogonal graph-manifolds is introduced. It is proved that the fundamental group of any orthogonal graph-manifold embeds quasiisometrically into a product of $ n$ trees. As a consequence, it is shown that the asymptotic dimension and the linearly-controlled asymptotic dimensions of such a group are equal to $ n$.

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Additional Information

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

Keywords: Graph-manifold, quasiisometric embedding
Received by editor(s): December 14, 2011
Published electronically: July 24, 2013
Additional Notes: Supported by RFBR (grant no. 11-01-00302-a)
Article copyright: © Copyright 2013 American Mathematical Society