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2017 An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds
Rudolf Zeidler
Algebr. Geom. Topol. 17(5): 3081-3094 (2017). DOI: 10.2140/agt.2017.17.3081

Abstract

We exhibit geometric situations where higher indices of the spinor Dirac operator on a spin manifold N are obstructions to positive scalar curvature on an ambient manifold M that contains N as a submanifold. In the main result of this note, we show that the Rosenberg index of N is an obstruction to positive scalar curvature on M if NM B is a fiber bundle of spin manifolds with B aspherical and π1(B) of finite asymptotic dimension. The proof is based on a new variant of the multipartitioned manifold index theorem which might be of independent interest. Moreover, we present an analogous statement for codimension-one submanifolds. We also discuss some elementary obstructions using the Â-genus of certain submanifolds.

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Rudolf Zeidler. "An index obstruction to positive scalar curvature on fiber bundles over aspherical manifolds." Algebr. Geom. Topol. 17 (5) 3081 - 3094, 2017. https://doi.org/10.2140/agt.2017.17.3081

Information

Received: 3 November 2016; Revised: 6 February 2017; Accepted: 26 February 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1377.58017
MathSciNet: MR3704253
Digital Object Identifier: 10.2140/agt.2017.17.3081

Subjects:
Primary: 58J22
Secondary: 46L80, 53C23

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.17 • No. 5 • 2017
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