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Hyperbolic rank of products


Foertsch, T; Schroeder, V (2005). Hyperbolic rank of products. Proceedings of the American Mathematical Society, 133(2):557-563.

Abstract

Generalizing results due to Brady and Farb we prove the existence of a bilipschitz embedded manifold of pinched negative curvature 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 pinched negative curvature. Combining this result with a Theorem by Buyalo and Schroeder we prove the additivity of the hyperbolic rank for products of manifolds with pinched negative curvature.

Abstract

Generalizing results due to Brady and Farb we prove the existence of a bilipschitz embedded manifold of pinched negative curvature 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 pinched negative curvature. Combining this result with a Theorem by Buyalo and Schroeder we prove the additivity of the hyperbolic rank for products of manifolds with pinched negative curvature.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Hadamard manifolds, hyperbolic rank
Language:English
Date:2005
Deposited On:27 Feb 2010 01:55
Last Modified:06 Dec 2017 20:46
Publisher:American Mathematical Society
ISSN:0002-9939
Additional Information:First published in [Proceedings of the American Mathematical Society] in [vol. 133, no. 2, 2005], published by the American Mathematical Society
Publisher DOI:https://doi.org/10.1090/S0002-9939-04-07598-7

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