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Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions.

Corro, Diego and Galaz-García, Fernando (2020) 'Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions.', Proceedings of the American Mathematical Society., 148 (7). pp. 3087-3097.

Abstract

We show that for each n 1, there exist infinitely many spin and non-spin diffeomorphism types of closed, smooth, simply-connected (n + 4)- manifolds with a smooth, effective action of a torus T n+2 and a metric of positive Ricci curvature invariant under a T n-subgroup of T n+2. As an application, we show that every closed, smooth, simply-connected 5- and 6-manifold admitting a smooth, effective torus action of cohomogeneity two supports metrics with positive Ricci curvature invariant under a circle or T2-action, respectively.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1090/proc/14961
Publisher statement:The deposited accepted manuscript is available under a Creative Commons CC-BY-NC-ND licence.
Date accepted:04 December 2019
Date deposited:05 February 2020
Date of first online publication:31 March 2020
Date first made open access:20 May 2020

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