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

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

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Authors

Marco Radeschi

Michael Wiemeler



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 Mar 28, 2024
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
Related Public URLs https://arxiv.org/abs/1404.3903

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Copyright Statement
This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record: Galaz-García, Fernando, Kerin, Martin, Radeschi, Marco & Wiemeler, Michael (2018). Torus Orbifolds, Slice-Maximal Torus Actions, and Rational Ellipticity. International Mathematics Research Notices 2018(18): 5786-5822 is available online at: https://doi.org/10.1093/imrn/rnx064.




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