Coarse cone quotients

Ulrich Bunke

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arXiv · 2507.01412

Coarse cone quotients

Ulrich Bunke

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Abstract

We study the coarse motive of the quotient $\mathcal{O}^{\infty}(X)//G$ of the cone of a uniform bornological coarse space $X$ with $G$-action. If $X$ admits a sufficiently ergodic probability measure, then we show that the coarse assembly map for $\mathcal{O}^{\infty}(X)//G$ is not an equivalence. The main ideas are taken from a recent paper by C. Kitsios, T. Schick and F. Vigolo (arXiv:2504.21811) and adapted to the formalism of coarse homotopy theory based on bornological coarse spaces developed by A. Engel and the author.

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Ulrich Bunke. 2025-07-02. Coarse cone quotients. https://arxiv.org/abs/2507.01412

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