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K-area bounds for smooth sphere bundles
Abstract
Let E→ B be a smooth Sn bundle with oriented Riemannian total space (E,g), where n≥2. We prove K-area(E,g)≤4πn(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)≤4π. 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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BibTeX
@misc{cheng2026karea,
title = {{K-area bounds for smooth sphere bundles}},
author = {Haoxuan Cheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.20440},
eprint = {2610.20440},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.20440},
}
RIS
TY - UNPB
TI - K-area bounds for smooth sphere bundles
AU - Haoxuan Cheng
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.20440
UR - https://arxiv.org/abs/2610.20440
AB - Let E→ B be a smooth S^n bundle with oriented Riemannian total space (E,g), where n≥2. We prove K-area(E,g)≤4πn(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)≤4π. 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.
ER -