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Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity

Galaz-García, Fernando and Kerin, Martin and Radeschi, Marco and Wiemeler, Michael (2018) 'Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity.', International Mathematics Research Notices, 2018 (18). pp. 5786-5822.

Abstract

In this work, it is shown that a simply connected, rationally elliptic torus orbifold is equivariantly rationally homotopy equivalent to the quotient of a product of spheres by an almost-free, linear torus action, where this torus has rank equal to the number of odd-dimensional spherical factors in the product. As an application, simply connected, rationally elliptic manifolds admitting slice-maximal torus actions are classified up to equivariant rational homotopy. The case where the rational-ellipticity hypothesis is replaced by non-negative curvature is also discussed, and the Bott Conjecture in the presence of a slice-maximal torus action is proved.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1093/imrn/rnx064
Publisher statement:This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record: Galaz-García, Fernando, Kerin, Martin, Radeschi, Marco & Wiemeler, Michael (2018). Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity. International Mathematics Research Notices 2018(18): 5786-5822 is available online at: https://doi.org/10.1093/imrn/rnx064.
Date accepted:17 February 2017
Date deposited:18 November 2022
Date of first online publication:24 March 2017
Date first made open access:18 November 2022

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