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.
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.
|Full text:||(AM) Accepted Manuscript|
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|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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