On hypersphericity of manifolds with finite asymptotic dimension
A Dranishnikov - Transactions of the American Mathematical Society, 2003 - ams.org
Transactions of the American Mathematical Society, 2003•ams.org
… We have defined here the notion of rational hypersphericity. One can define integral
hypersphericity by taking into account only maps of degree one. A further generalization
consists of replacing the n-sphere by Rn. It leads to the notion of hypereuclidean … Let M
be a closed aspherical manifold and assume that the fundamental group Γ = π1(M) as a
metric space with the word metric has finite asymptotic dimension asdim Γ < ∞. Then M
cannot carry a metric with a positive scalar curvature. …
hypersphericity by taking into account only maps of degree one. A further generalization
consists of replacing the n-sphere by Rn. It leads to the notion of hypereuclidean … Let M
be a closed aspherical manifold and assume that the fundamental group Γ = π1(M) as a
metric space with the word metric has finite asymptotic dimension asdim Γ < ∞. Then M
cannot carry a metric with a positive scalar curvature. …
Abstract
We prove the following embedding theorems in the coarse geometry:
Theorem A. Every metric space with bounded geometry whose asymptotic dimension does not exceed admits a large scale uniform embedding into the product of locally finite trees.
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