Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity

Galaz-García, 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.

Citation

Galaz-García, F., Kerin, M., Radeschi, M., & Wiemeler, M. (2018). Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity. International Mathematics Research Notices, 2018(18), 5786-5822. https://doi.org/10.1093/imrn/rnx064

• Journal Article Type: Article
• Acceptance Date: Feb 17, 2017
• Online Publication Date: Mar 24, 2017
• Publication Date: 2018-09
• Deposit Date: Dec 12, 2019
• Publicly Available Date: Nov 18, 2022
• Journal: International Mathematics Research Notices
• Print ISSN: 1073-7928
• Electronic ISSN: 1687-0247
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 2018
• Issue: 18
• Pages: 5786-5822
• DOI: https://doi.org/10.1093/imrn/rnx064
• Public URL: https://durham-repository.worktribe.com/output/1275313
• Related Public URLs: https://arxiv.org/abs/1404.3903