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Regularity of limits of noncollapsing sequences of manifolds

Vitali Kapovitch
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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 $X^n$ with $n\ge 5$ there exists an Alexandrov space $Y$ homeomorphic to $X$ which can not be obtained as such a limit.

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Vitali Kapovitch. 2001-09-11. Regularity of limits of noncollapsing sequences of manifolds. https://arxiv.org/abs/math/0109075

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