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arXiv · 2602.06666

Quantitative partitioned index theorem and noncompact band-width

Peter Hochs·Jinmin Wang
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Abstract

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.

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Peter Hochs, Jinmin Wang. 2026-02-06. Quantitative partitioned index theorem and noncompact band-width. https://arxiv.org/abs/2602.06666

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