A Product Formula for Family Indices and Family Band Width Estimates

2025/07/29 by Song, Chenkai
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.21594

Abstract

We extend Gromov's conjecture on the sharp width estimate for Riemannian bands with positive scalar curvature to the family case and prove that it holds for fiber bundles with infinite family A-hat area. The method we employ is based on Dirac operators and the family index theory. Our proof relies on a product formula for index bundles established in this paper.

Citations

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• A proof of Gromov's cube inequality on scalar curvature
• Width estimate and doubly warped product
• A long neck principle for Riemannian spin manifolds with positive scalar\n curvature
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Related

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• Width estimate and doubly warped product
• Infinite connected sums, K-area and positive scalar curvature
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• On distance estimates for complete manifolds with lower scalar curvature bounds