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arXiv · 1404.3903

Torus orbifolds, slice-maximal torus actions and rational ellipticity

Fernando Galaz-Garcia·Martin Kerin·Marco Radeschi·Michael Wiemeler
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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.

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Fernando Galaz-Garcia, Martin Kerin, Marco Radeschi, Michael Wiemeler. 2015-11-26. Torus orbifolds, slice-maximal torus actions and rational ellipticity. https://doi.org/10.1093/imrn%2Frnx064

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