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On fibers of fat associated bundles

Volume 150 / 2017

Maciej Bocheński, Anna Szczepkowska, Aleksy Tralle, Artur Woike Colloquium Mathematicum 150 (2017), 149-159 MSC: Primary 57S30; Secondary 22F30, 22E40, 22E46. DOI: 10.4064/cm7138s-1-2017 Published online: 1 September 2017

Abstract

We are interested in associated fat bundles, which are an important tool in constructing Riemannian metrics of positive and non-negative curvature. We want to understand the behavior of the fatness condition under changes of structure groups of bundles. We show that if the structure group does not coincide with the holonomy group, and the $G$-bundle is fat, then the fiber of the bundle must be finitely covered by a sphere or a complex projective space of a particular dimension.

Authors

  • Maciej BocheńskiDepartment of Mathematics and Computer Science
    University of Warmia and Mazury
    Słoneczna 54
    10-710 Olsztyn, Poland
    e-mail
  • Anna SzczepkowskaDepartment of Mathematics and Computer Science
    University of Warmia and Mazury
    Słoneczna 54
    10-710 Olsztyn, Poland
    e-mail
  • Aleksy TralleDepartment of Mathematics and Computer Science
    University of Warmia and Mazury
    Słoneczna 54
    10-710 Olsztyn, Poland
    e-mail
  • Artur WoikeDepartment of Mathematics and Computer Science
    University of Warmia and Mazury
    Słoneczna 54
    10-710 Olsztyn, Poland
    e-mail

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