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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Dimensions of products of hyperbolic spaces


Author: N. Lebedeva
Translated by: the author
Original publication: Algebra i Analiz, tom 19 (2007), nomer 1.
Journal: St. Petersburg Math. J. 19 (2008), 107-124
MSC (2000): Primary 54F45
Published electronically: December 17, 2007
MathSciNet review: 2319513
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Abstract | References | Similar Articles | Additional Information

Abstract: Estimates on asymptotic dimension are given for products of general hyperbolic spaces, with applications to hyperbolic groups. Examples are presented where strict inequality occurs in the product theorem for the asymptotic dimension in the class of hyperbolic groups and in the product theorem for the hyperbolic dimension. It is proved that $ \mathbb{R}$ is dimensionally full for the asymptotic dimension in the class of hyperbolic groups.


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Additional Information

N. Lebedeva
Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: lebed@pdmi.ras.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-07-00988-0
PII: S 1061-0022(07)00988-0
Keywords: Asymptotic dimension, hyperbolic groups, linearly controlled dimension, quasi-isometry invariants.
Received by editor(s): June 19, 2007
Published electronically: December 17, 2007
Additional Notes: Supported by RFBR (grant no. 05-01-00939)
Dedicated: To dear Viktor Abramovich Zalgaller on the occasion of his 85th birthday
Article copyright: © Copyright 2007 American Mathematical Society