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Seminários do IMPA

Geometria Diferencial

Título |
Non-negatively curved vector bundles over cohomogeneity one manifolds |

Expositor |
Manuel Amann
Augsburg University |

Data |
Terça-feira, 11 de fevereiro de 2020, 15:30 |

Local |
Sala 236 |

Resumo |

Generalizing homogeneous spaces, it was proved by GroveZiller that cohomogeneity one manifolds under certain restrictions provide an important class of spaces which admit metrics of non-negative sectional curvature.

On these manifolds we identify conditions under which vector bundles over them (up to suitable stabilizations) admit metrics of non-negative sectional curvature as well--thus providing a certain converse to the soul theorem. We achieve this by relating the bundles to equivariant ones up to stabilization.

Beside constructions of bundle metrics, we essentially draw on K-theory computations to obtain the result. Moreover, we use the connection between (rational) K-theory and cohomology in order to link equivariant K-theory to equivariant (singular) cohomology--investigating the latter via rational homotopy theory. These methods are also applied to answer related open questions concerning the (equivariant) K-theory of homogeneous spaces.

This talk reports on joint work with David Gonzalez-Alvaro and Marcus Zibrowius.