2017
Том 69
№ 9

All Issues

On fundamental group of Riemannian manifolds with ommited fractal subsets

Mirzaie R.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 6, pp 993-998.

Citation Example: Mirzaie R. On fundamental group of Riemannian manifolds with ommited fractal subsets // Ukr. Mat. Zh. - 2011. - 63, № 6. - pp. 854-858.

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