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


Latschev, J (2001). Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold. Archiv der Mathematik, 77(6):522-528.

Abstract

We show that for every closed Riemannian manifold X there exists a positive number¶ ε0>0 such that for all 0< there exists some¶ δ>0 such that for every metric space Y with Gromov-Hausdorff distance to X less than¶ δ the geometric ε -complex |Yε| is homotopy equivalent to X.¶ In particular, this gives a positive answer to a question of Hausmann.

Abstract

We show that for every closed Riemannian manifold X there exists a positive number¶ ε0>0 such that for all 0< there exists some¶ δ>0 such that for every metric space Y with Gromov-Hausdorff distance to X less than¶ δ the geometric ε -complex |Yε| is homotopy equivalent to X.¶ In particular, this gives a positive answer to a question of Hausmann.

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15 citations in Web of Science®
14 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:Gromov-Hausdorff distance; pseudo-metric space; simplicial complex
Language:English
Date:2001
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:25
Publisher:Springer
ISSN:0003-889X
Publisher DOI:https://doi.org/10.1007/PL00000526
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1001.53026
http://www.ams.org/mathscinet-getitem?mr=1879057

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