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A Thorpe Trick for the Bochner Technique
Abstract
We prove that for n ≥ 6 there exists ε (n)>0 such that every closed orientable Riemannian manifold with ( ⌈ n/2 ⌉+ ε)-positive curvature operator is a real homology sphere. For n=6 we show that the same result holds for manifolds with $4$-positive curvature operators.
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BibTeX
@misc{wink2026thorpe,
title = {{A Thorpe Trick for the Bochner Technique}},
author = {Matthias Wink},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11653},
eprint = {2609.11653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11653},
}
RIS
TY - UNPB
TI - A Thorpe Trick for the Bochner Technique
AU - Matthias Wink
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11653
UR - https://arxiv.org/abs/2609.11653
AB - We prove that for n ≥ 6 there exists ε (n)>0 such that every closed orientable Riemannian manifold with ( ⌈ n/2 ⌉+ ε)-positive curvature operator is a real homology sphere. For n=6 we show that the same result holds for manifolds with $4$-positive curvature operators.
ER -