Coarse structures on groups

Andrew Nicas; David Rosenthal

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arXiv · 1201.4687

Coarse structures on groups

Andrew Nicas·David Rosenthal

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Abstract

We introduce the group-compact coarse structure on a Hausdorff topological group in the context of coarse structures on an abstract group which are compatible with the group operations. We develop asymptotic dimension theory for the group-compact coarse structure generalizing several familiar results for discrete groups. We show that the asymptotic dimension in our sense of the free topological group on a non-empty topological space that is homeomorphic to a closed subspace of a Cartesian product of metrizable spaces is 1.

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Andrew Nicas, David Rosenthal. 2012-01-23. Coarse structures on groups. https://arxiv.org/abs/1201.4687

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