Impossible metric conditions on exotic R^4's

Laurence R. Taylor

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Impossible metric conditions on exotic R^4's

Laurence R. Taylor

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Abstract

There are many theorems in the differential geometry literature of the following sort. Let M be a complete Riemannian manifold with some conditions on various curvatures, diameters, volumes, etc. Then M is homotopy equivalent to a finite CW complex, or M is the interior of a compact, topological manifold with boundary. At first glance it seems unlikely that such theorems have anything to say about smooth manifolds homeomorphic to R^4. However, there is a common theme to all the proofs which forbids the existence of such metrics on most (and possibly all) exotic R^4's.

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BibTeX RIS

Laurence R. Taylor. 2005-10-21. Impossible metric conditions on exotic R^4's. https://arxiv.org/abs/math/0510450

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