Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds

Philipp Reiser; Masoumeh Zarei

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arXiv · 2609.10268

Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds

Philipp Reiser·Masoumeh Zarei

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Abstract

We prove a vanishing theorem for the local Betti numbers of closed, $n$-dimensional Riemannian manifolds with a lower volume bound, an upper diameter bound, and a lower intermediate Ricci curvature bound. This generalizes and interpolates between known results under lower sectional and Ricci curvature bounds. Moreover, the methods extend to open manifolds, yielding a corresponding vanishing theorem for the global Betti numbers.

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Philipp Reiser, Masoumeh Zarei. 2026-09-09. Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds. https://arxiv.org/abs/2609.10268

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