Band Width and the Rosenberg Index

DOI10.1093/IMRN/RNAC124zbMATH Open1521.19002arXiv2108.08506OpenAlexW4225505730MaRDI QIDQ6097882

Yosuke Kubota

Publication date: 7 June 2023

Published in: IMRN. International Mathematics Research Notices (Search for Journal in Brave)

Abstract: A Riemannian manifold is said to have infinite $mathcalKO$-width if it admits an isometric immersion of an arbitrarily wide Riemannian band whose inward boundary has non-trivial higher index. In this paper we prove that if a closed spin manifold has inifinite $mathcalKO$-width, then its Rosenberg index does not vanish. This gives a positive answer to a conjecture by R. Zeidler. We also prove its `multi-dimensional' generalization; if a closed spin manifold admit an isometric immersion of an arbitrarily wide cube-like domain whose lowest dimensional corner has non-trivial higher index, then the Rosenberg index of $M$ does not vanish.

Full work available at URL: https://arxiv.org/abs/2108.08506

zbMATH Keywords

\(K\)-theorypositive scalar curvaturehigher index theory

Mathematics Subject Classification ID

Exotic index theories on manifolds (58J22) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) (57R15) Index theory (19K56)

Related Items (3)

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