Regularity of limits of noncollapsing sequences of manifolds

Vitali Kapovitch

Regularity of limits of noncollapsing sequences of manifolds

Differential Geometry 2016-09-07 v1 Metric Geometry

Authors: Vitali Kapovitch

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 can not be obtained as such a limit.

Keywords

noncollapsing sequence manifold alexandrov space space of directions lower curvature bound topological sphere

Cite

@article{arxiv.math/0109075,
  title  = {Regularity of limits of noncollapsing sequences of manifolds},
  author = {Vitali Kapovitch},
  journal= {arXiv preprint arXiv:math/0109075},
  year   = {2016}
}

Comments

17 pages, to appear in GAFA

Related papers

View all related →