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