English

Quantitative partitioned index theorem and noncompact band-width

Differential Geometry 2026-02-09 v1 K-Theory and Homology Operator Algebras

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.

Keywords

Cite

@article{arxiv.2602.06666,
  title  = {Quantitative partitioned index theorem and noncompact band-width},
  author = {Peter Hochs and Jinmin Wang},
  journal= {arXiv preprint arXiv:2602.06666},
  year   = {2026}
}

Comments

46 pages

R2 v1 2026-07-01T10:24:19.022Z