Coarsely separation of groups and spaces

Panagiotis Tselekidis

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arXiv · 2403.15892

Coarsely separation of groups and spaces

Panagiotis Tselekidis

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Abstract

Inspired by a classical theorem of topological dimension theory, we prove that every geodesic metric space of asymptotic dimension $n$ containing a bi-infinite geodesic can be coarsely separated by a subset $S$ of asymptotic dimension equal to or smaller than $n-1$.\\ We define asymptotic Cantor manifolds, and we prove that every finitely generated group contains such a manifold. We also state some questions related to them.

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Panagiotis Tselekidis. 2024-03-23. Coarsely separation of groups and spaces. https://arxiv.org/abs/2403.15892

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