English

Restrictions on collapsing with a lower sectional curvature bound

Differential Geometry 2007-05-23 v1 Metric Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.math/0110087,
  title  = {Restrictions on collapsing with a lower sectional curvature bound},
  author = {Vitali Kapovitch},
  journal= {arXiv preprint arXiv:math/0110087},
  year   = {2007}
}
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