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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.21594 |
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Table of Contents:
- 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.