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


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].


Riemannian Manifold Positive Answer Homotopy Equivalent Closed Riemannian Manifold 
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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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