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arXiv · 2610.40062

Higher-order jet and its application to the Novikov conjecture

Jintao Deng·Geng Tian
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Abstract

In this paper, we apply higher-order tangent bundles and higher-order derivative maps to study countable subgroups of the deffeomorphism group ${\rm Diff}(M)$ of a closed smooth manifold $M$. Using this framework, we introduce the concept of higher order $μ$-discreteness for subgroup $Γ< {\rm Diff}(M)$. As applications, we show that both the strong Novikov conjecture and the coarse Baum--Connes conjecture hold for countable groups with higher order $μ$-discreteness.

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Jintao Deng, Geng Tian. 2026-10-29. Higher-order jet and its application to the Novikov conjecture. https://arxiv.org/abs/2610.40062

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