Torus orbifolds, slice-maximal torus actions and rational ellipticity

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.

A gap in the first version has been fixed and the paper has been substantially expanded. Several new results have been added. The title and abstract have been changed accordingly. 36 pages, 1 figure

References in corpus (2)

• Torus manifolds and non-negative curvature
• Non-negative curvature and torus actions

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