Coarse property {C} and decomposition complexity

Gregory Bell; Danielle Moran; Andrzej Nagórko

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arXiv · 1604.02405

Coarse property {C} and decomposition complexity

Gregory Bell·Danielle Moran·Andrzej Nagórko

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Abstract

The coarse category was established by Roe to distill the salient features of the large-scale approach to metric spaces and groups that was started by Gromov. In this paper, we use the language of coarse spaces to define coarse versions of asymptotic property C and decomposition complexity. We prove that coarse property C implies coarse property A; we also show that these coarse versions share many of the features of their metric analogs such as preservation by products or unions.

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Gregory Bell, Danielle Moran, Andrzej Nagórko. 2016-04-08. Coarse property {C} and decomposition complexity. https://arxiv.org/abs/1604.02405

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