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arXiv · 2511.17751

Almost positively curved generalized Eschenburg spaces

Jason DeVito·Joan West
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Abstract

In each dimension of the form $4n-1$ with $n\geq 3$, we construct infinitely many new examples of manifolds admitting metrics with positive sectional curvature almost everywhere. In addition, we show that if $n\geq 6$, infinitely many of our examples are not homotopy equivalent to any homogeneous space, providing the first infinite family of such examples.

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Jason DeVito, Joan West. 2025-11-21. Almost positively curved generalized Eschenburg spaces. https://arxiv.org/abs/2511.17751

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