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Hyperbolic rank of products

Author(s): Thomas Foertsch; Viktor Schroeder
Journal: Proc. Amer. Math. Soc. 133 (2005), 557-563.
MSC (2000): Primary 53C20
Posted: August 25, 2004
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Abstract: Generalizing a result of Brady and Farb (1998), we prove the existence of a bilipschitz embedded manifold of negative curvature bounded away from zero and dimension $m_1+m_2-1$ in the product $X:=X_1^{m_1}\times X_2^{m_2}$ of two Hadamard manifolds $X_i^{m_i}$ of dimension $m_i$ with negative curvature bounded away from zero.

Combining this result with a result of Buyalo and Schroeder (2002), we prove the additivity of the hyperbolic rank for products of manifolds with negative curvature bounded away from zero.

References:

[BuySch]
S.Buyalo & V.Schroeder, Hyperbolic rank and subexponential corank of metric spaces, Geom. Funct. Anal., vol. 12, no.2 (2002), 293-306. MR 2003e:53045

[BrFa]
N.Brady & B. Farb, Filling-Invariants at Infinity for Manifolds of Nonpositive Curvature, Trans. Amer. Math. Soc., vol. 350, no. 8, (1998), 3393-3405. MR 99c:53039

[Foe]
T.Foertsch, Bilipschitz Embeddings of Negative Sectional Curvature in Products of Warped Product Manifolds, Proc. Amer. Math. Soc., vol.130, no.7 (2002), 2089-2096. MR 2003b:53041

[Gr]
M.Gromov, Asymptotic invariants of infinite groups, Geometric Group theory. Editors: Niblo, Roller, London Math. Soc., Lecture Notes Series 182 Vol.2, Cambridge University Press, 1993. MR 95m:20041

[Leu]
E.Leuzinger, Corank and Asymptotic Filling-Invariants for Symmetric Spaces, Geom. Funct. Anal., vol.10, no.4 (2000), 863-873. MR 2001k:53074

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Additional Information:

Thomas Foertsch
Affiliation: Universität Zürich, Mathematisches Institut, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
Address at time of publication: Department of Mathematics, University of Michigan, 525 E University Avenue, East Hall, Ann Arbor, Michigan 48109-1109
Email: foertsch@math.unizh.ch

Viktor Schroeder
Affiliation: Universität Zürich, Mathematisches Institut, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
Email: vschroed@math.unizh.ch

DOI: 10.1090/S0002-9939-04-07598-7
PII: S 0002-9939(04)07598-7
Keywords: Hadamard manifolds, hyperbolic rank
Received by editor(s): December 19, 2001
Received by editor(s) in revised form: April 29, 2003
Posted: August 25, 2004
Additional Notes: The first author was supported by the SNF Grant 21 - 589 38.99
Communicated by: Wolfgang Ziller
Copyright of article: Copyright 2004, American Mathematical Society

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