Hyperbolic Rank of Products
Abstract
Generalizing results due to Brady and Farb we prove the existence of a bilipschitz embedded manifold of pinched negative curvature and dimension m1+m2-1 in the product X:=X1m1 times X2m2 of two Hadamard manifolds Ximi of dimension mi 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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