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Seminários do IMPA

Geometria Diferencial

Título |
$\Gamma$-structures and symmetric spaces |

Expositor |
Bernhard Hanke
University of Augsburg |

Data |
Terça-feira, 9 de janeiro de 2018, 15:30 |

Local |
Sala 236 |

Resumo |

$\Gamma$-structures are weak forms of multiplications on closed oriented manifolds. As shown by Hopf the rational cohomology algebras of manifolds admitting $\Gamma$-structures are free over odd degree generators. We prove that this condition is also sufficient for the existence of $\Gamma$-structures on manifolds which are nilpotent in the sense of homotopy theory. This includes homogeneous spaces with connected isotropy groups.

Passing to a more geometric perspective we show that on compact oriented Riemannian symmetric spaces with connected isotropy groups and free rational cohomology algebras the canonical products given by geodesic symmetries define $\Gamma$-structures. This extends work of Albers, Frauenfelder, and Solomon on $\Gamma$-structures on Lagrangian Grassmannians.