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Non-Negative Curvature, Elliptic Genus and Unbounded Pontryagin Numbers

Part of: Global differential geometry Differential topology

Published online by Cambridge University Press:  26 February 2018

Martin Herrmann  and
Nicolas Weisskopf
Martin Herrmann*
Affiliation:
Fakultät für Mathematik, Karlsruher Institut für Technologie, Kaiserstraße 89–93, 76133 Karlsruhe, Germany (martin.herrmann@riemannian-topology.de)
Nicolas Weisskopf
Affiliation:
Département de Mathématiques, Université de Fribourg, Chemin du Musée 23, 1700 Fribourg, Switzerland (nic.weisskopf@gmail.com)
*
*Corresponding author.
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Abstract

We discuss the cobordism type of spin manifolds with non-negative sectional curvature. We show that in each dimension 4k ⩾ 12, there are infinitely many cobordism types of simply connected and non-negatively curved spin manifolds. Moreover, we raise and analyse a question about possible cobordism obstructions to non-negative curvature.

Keywords

non-negative curvaturespin manifoldselliptic genusPontryagin numbers

MSC classification

Primary: 53C20: Global Riemannian geometry, including pinching
Secondary: 57R75: ${rm O}$- and ${rm SO}$-cobordism
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 2 , May 2018 , pp. 449 - 456
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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