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arXiv · 1911.02338

Controlled objects in left-exact $\infty$-categories and the Novikov conjecture

Ulrich Bunke·Denis-Charles Cisinski·Daniel Kasprowski·Christoph Winges
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Abstract

We associate to every $G$-bornological coarse space $X$ and every left-exact $\infty$-category with $G$-action a left-exact infinity-category of equivariant $X$-controlled objects. Postcomposing with algebraic K-theory leads to {new} equivariant coarse homology theories. This allows us to apply the injectivity results for assembly maps by Bunke, Engel, Kasprowski and Winges to the algebraic K-theory of left-exact $\infty$-categories.

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Ulrich Bunke, Denis-Charles Cisinski, Daniel Kasprowski, Christoph Winges. 2019-11-06. Controlled objects in left-exact $\infty$-categories and the Novikov conjecture. https://arxiv.org/abs/1911.02338

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