Permanent URL to this publication: http://dx.doi.org/10.5167/uzh-21934
Buyalo, S; Schroeder, V (2002). Hyperbolic rank and subexponential corank of metric spaces. Geometric and Functional Analysis, 12(2):293-306.
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We introduce a new quasi-isometry invariant corank X of a metric space X called subexponential corank. A metric space X has subexponential corank k if roughly speaking there exists a continuous map , T is a topological space, such that for each the set g -1(t) has subexponential growth rate in X and the topological dimension dimT = k is minimal among all such maps. Our main result is the inequality for a large class of metric spaces X including all locally compact Hadamard spaces, where rank h X is the maximal topological dimension of among all CAT(—1) spaces Y quasi-isometrically embedded into X (the notion introduced by M. Gromov in a slightly stronger form). This proves several properties of rank h conjectured by Gromov, in particular, that any Riemannian symmetric space X of noncompact type possesses no quasi-isometric embedding of the standard hyperbolic space H n with n – 1 > dim X – rank X.
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|Item Type:||Journal Article, refereed, original work|
|Communities & Collections:||07 Faculty of Science > Institute of Mathematics|
|Deposited On:||29 Nov 2010 16:27|
|Last Modified:||17 Dec 2013 10:39|
|Additional Information:||The original publication is available at www.springerlink.com|
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