Regularity of limits of noncollapsing sequences of manifolds

Details Regularity of limits of noncollapsing sequences of manifolds Regularity of limits of noncollapsing sequences of manifolds

2001-09-11

arxiv.org/abs/math/0109075v1

Mathematics

Differential Geometry

17 pages, to appear in GAFA

Scientific paper

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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