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Torus orbifolds, slice-maximal torus actions and rational ellipticity. [Preprint]

Galaz-Garcia, Fernando; Kerin, Martin; Radeschi, Marco; Wiemeler, Michael

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.


Zugehörige Institution(en) am KIT Institut für Algebra und Geometrie (IAG)
Publikationstyp Buchaufsatz
Jahr 2014
Sprache Englisch
Identifikator KITopen ID: 1000051184
Erschienen in arXiv [math.DG]
Seiten arXiv:1404.3903
URLs http://arxiv.org/abs/1404.3903
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