On fundamental group of Riemannian manifolds with ommited fractal subsets

• Date: 2011
• Main Authors: Mirzaie, R., Мірзай, Р.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2769
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.