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arXiv · 2412.01314

Quantitative index, Novikov conjecture and coarse decomposability

Hervé Oyono-Oyono·Guoliang Yu
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Abstract

We define for families of finite metric spaces quantitative assembly map estimates that take into account propagation phenomena for pseudo-differential calculus. We relate these estimates to the Novikov conjecture and we show that they fit nicely under coarse decompositions. As an application, we provide a geometric proof of Novikov conjecture for groups with finite decomposition complexity.

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Hervé Oyono-Oyono, Guoliang Yu. 2024-12-02. Quantitative index, Novikov conjecture and coarse decomposability. https://arxiv.org/abs/2412.01314

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