On Large Scale Properties of Manifolds

Details On Large Scale Properties of Manifolds On Large Scale Properties of Manifolds

1999-12-08

arxiv.org/abs/math/9912062v1

Mathematics

Geometric Topology

11 pages

Scientific paper

We show that a space with a finite asymptotic dimension is embeddable in a non-positively curved manifold. Then we prove that if a uniformly contractible manifold X is uniformly embeddable in $\R^n$ or non-positively curved n-dimensional simply connected manifold then $X\times\R^n$ is integrally hyperspherical. If a uniformly contractible manifold X of bounded geometry is uniformly embeddable into a Hilbert space, then X is stably integrally hyperspherical.

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