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Coarse Baum-Connes and warped cones: failure of surjectivity in odd degree

· 2025 · math.KT · arXiv 2504.21811

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abstract

We prove a conjecture of Roe by constructing unified warped cones that violate the coarse Baum-Connes conjecture. Interestingly, the reason for this is probably not what Roe expected, as the obstruction arises in odd rather than even degree.

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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 16 · 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.