Torus orbifolds, slicemaximal torus actions and rational ellipticity
Abstract
In this work, it is shown that a simplyconnected, rationallyelliptic torus orbifold is equivariantly rationally homotopy equivalent to the quotient of a product of spheres by an almostfree, linear torus action, where this torus has rank equal to the number of odddimensional spherical factors in the product. As an application, simplyconnected, rationallyelliptic manifolds admitting slicemaximal torus actions are classified up to equivariant rational homotopy. The case where the rationalellipticity hypothesis is replaced by nonnegative curvature is also discussed, and the Bott Conjecture in the presence of a slicemaximal torus action is proved.
 Publication:

arXiv eprints
 Pub Date:
 April 2014
 DOI:
 10.48550/arXiv.1404.3903
 arXiv:
 arXiv:1404.3903
 Bibcode:
 2014arXiv1404.3903G
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Geometric Topology;
 55P62;
 57S10
 EPrint:
 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