Homotopy theory with bornological coarse spaces

Ulrich Bunke; Alexander Engel

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arXiv · 1607.03657

Homotopy theory with bornological coarse spaces

Ulrich Bunke·Alexander Engel

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Abstract

We propose an axiomatic characterization of coarse homology theories defined on the category of bornological coarse spaces. We construct a category of motivic coarse spectra. Our focus is the classification of coarse homology theories and the construction of examples. We show that if a transformation between coarse homology theories induces an equivalence on all discrete bornological coarse spaces, then it is an equivalence on bornological coarse spaces of finite asymptotic dimension. The example of coarse K-homology will be discussed in detail.

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Ulrich Bunke, Alexander Engel. 2016-07-13. Homotopy theory with bornological coarse spaces. https://arxiv.org/abs/1607.03657

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