Latschev, J (2001). Vietoris-Rips complexes of metric spaces near a closed Riemannian manifold. Archiv der Mathematik, 77(6):522-528.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics |
| Uncontrolled Keywords: | Gromov-Hausdorff distance, pseudo-metric space, simplicial complex |
| Language: | English |
| Date: | 2001 |
| Deposited On: | 29 Nov 2010 16:27 |
| Last Modified: | 23 Jan 2022 14:40 |
| Publisher: | Springer |
| ISSN: | 0003-889X |
| OA Status: | Closed |
| 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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Latschev, J