Restrictions on collapsing with a lower sectional curvature bound

Details Restrictions on collapsing with a lower sectional curvature bound Restrictions on collapsing with a lower sectional curvature bound

2001-10-08

arxiv.org/abs/math/0110087v1

Mathematics

Differential Geometry

Scientific paper

We obtain new topological information about the local structure of collapsing
under a lower sectional curvature bound. As an application we prove a new
sphere theorem and obtain a partial result towards the conjecture that not
every Alexandrov space can be obtained as a limit of a sequence of Riemannian
manifolds with sectional curvature bounded from below.

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