Quantitative partitioned index theorem and noncompact band-width
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915779976364032 |
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| author | Hochs, Peter Wang, Jinmin |
| author_facet | Hochs, Peter Wang, Jinmin |
| contents | Gromov's band-width conjecture gives a precise upper bound for the width of a compact Riemannian band with positive scalar curvature lower bound, assuming that the cross-section of the band admits no positive scalar curvature metrics. Versions of this were proved by Cecchini and by Zeidler. In this paper, we develop a quantitative version of partitioned manifold index theory, which applies to noncompact hypersurfaces. Using this, we prove a version of Gromov's band-width estimate for possibly noncompact Riemannian bands. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06666 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative partitioned index theorem and noncompact band-width Hochs, Peter Wang, Jinmin Differential Geometry K-Theory and Homology Operator Algebras Gromov's band-width conjecture gives a precise upper bound for the width of a compact Riemannian band with positive scalar curvature lower bound, assuming that the cross-section of the band admits no positive scalar curvature metrics. Versions of this were proved by Cecchini and by Zeidler. In this paper, we develop a quantitative version of partitioned manifold index theory, which applies to noncompact hypersurfaces. Using this, we prove a version of Gromov's band-width estimate for possibly noncompact Riemannian bands. |
| title | Quantitative partitioned index theorem and noncompact band-width |
| topic | Differential Geometry K-Theory and Homology Operator Algebras |
| url | https://arxiv.org/abs/2602.06666 |