Regularity of limits of noncollapsing sequences of manifolds
Abstract
We prove that iterated spaces of directions of a limit of a noncollapsing sequence of manifolds with lower curvature bound are topologically spheres. As an application we show that for any finite dimensional Alexandrov space Xn with n 5 there exists an Alexandrov space Y homeomorphic to X which can not be obtained as such a limit.
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