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arXiv · 2610.20440

K-area bounds for smooth sphere bundles

Haoxuan Cheng
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Abstract

Let $E\to B$ be a smooth $S^n$ bundle with oriented Riemannian total space $(E,g)$, where $n\ge2$. We prove K-area$(E,g)\le4πn(n-1)/σ$ whenever every fibre has intrinsic scalar curvature at least $σ>0$, independently of the dimension of $B$. In particular, unit round fibres give K-area$(E,g)\le4π$. For arbitrary metrics on two-sphere fibres, K-area is bounded by the supremum of their areas. We also obtain stronger bounds from fibrewise scalar spectra.

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Haoxuan Cheng. 2026-10-14. K-area bounds for smooth sphere bundles. https://arxiv.org/abs/2610.20440

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