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 cannot be obtained as such a limit.
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Submitted: December 2000, Revised: March 2001.
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Kapovitch, V. Regularity of limits of noncollapsing sequences of manifolds . GAFA, Geom. funct. anal. 12, 121–137 (2002). https://doi.org/10.1007/s00039-002-8240-1
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DOI: https://doi.org/10.1007/s00039-002-8240-1