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Archiv der Mathematik

, Volume 77, Issue 6, pp 522–528 | Cite as

Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold

  • J. Latschev

Abstract.

We show that for every closed Riemannian manifold X there exists a positive number¶\( \varepsilon_0 > 0 \) such that for all 0< \( \varepsilon \leqq \varepsilon_0 \) there exists some¶\( \delta > 0 \) such that for every metric space Y with Gromov-Hausdorff distance to X less than¶\( \delta \) the geometric \( \varepsilon \)-complex \( |Y_\varepsilon| \) is homotopy equivalent to X.¶ In particular, this gives a positive answer to a question of Hausmann [4].

Keywords

Riemannian Manifold Positive Answer Homotopy Equivalent Closed Riemannian Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • J. Latschev
    • 1
  1. 1.Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland, janko@math.unizh.chCH

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