On fundamental group of Riemannian manifolds with ommited fractal subsets
We show that if $K$ is a closed and bounded subset of a Riemannian manifold $M$ of dimension $m > 3$, and the fractal dimension of $K$ is less than $m - 3$, then the fundamental groups of $M$ and $M - K$ are isomorphic.
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| Datum: | 2011 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2011
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2769 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | We show that if $K$ is a closed and bounded subset of a Riemannian manifold $M$ of dimension $m > 3$, and the fractal dimension of $K$ is less than $m - 3$, then the fundamental groups of $M$ and $M - K$ are isomorphic. |
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