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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