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May 2020 Highly connected 7-manifolds and non-negative sectional curvature
S. Goette, M. Kerin, K. Shankar
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Ann. of Math. (2) 191(3): 829-892 (May 2020). DOI: 10.4007/annals.2020.191.3.3

Abstract

In this article, a six-parameter family of highly connected 7-manifolds which admit an $\mathrm{SO}(3)$-invariant metric of non-negative sectional curvature is constructed and the Eells-Kuiper invariant of each is computed. In particular, it follows that all exotic spheres in dimension 7 admit an $\mathrm{SO}(3)$-invariant metric of non-negative curvature.

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S. Goette. M. Kerin. K. Shankar. "Highly connected 7-manifolds and non-negative sectional curvature." Ann. of Math. (2) 191 (3) 829 - 892, May 2020. https://doi.org/10.4007/annals.2020.191.3.3

Information

Published: May 2020
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2020.191.3.3

Subjects:
Primary: 53C20
Secondary: 57R20 , 57R55 , 58J28

Keywords: Eells-Kuiper invariant , exotic sphere , highly connected $7$-manifold , non-negative curvature

Rights: Copyright © 2020 Department of Mathematics, Princeton University

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Vol.191 • No. 3 • May 2020
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