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Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds
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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BibTeX
@misc{reiser2026local,
title = {{Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds}},
author = {Philipp Reiser and Masoumeh Zarei},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10268},
eprint = {2609.10268},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10268},
}
RIS
TY - UNPB
TI - Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds
AU - Philipp Reiser
AU - Masoumeh Zarei
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10268
UR - https://arxiv.org/abs/2609.10268
AB - 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.
ER -