Restrictions on collapsing with a lower sectional curvature bound

2001/10/08 by Vitali Kapovitch, Kapovitch, Vitali
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.DG #math.MG #msc:53C20

paper · pdf · doi:10.48550/arxiv.math/0110087

arxiv created 2001/10/08 · arxiv updated 2009/11/30

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.

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