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

· 2019 · math.KT · arXiv 1911.02338

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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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math.AT 1

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2025 1

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CONDITIONAL 1

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Coarse cone quotients

math.AT · 2025-07-02 · conditional · novelty 6.0

For uniformly free, ergodic actions with spectral gap, the motivic coarse assembly map for the cone quotient O∞(X)//G fails to be an equivalence.

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  • Coarse cone quotients math.AT · 2025-07-02 · conditional · none · ref 1 · internal anchor

    For uniformly free, ergodic actions with spectral gap, the motivic coarse assembly map for the cone quotient O∞(X)//G fails to be an equivalence.