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Seminários do IMPA

Geometria Diferencial

Non-negatively curved vector bundles over cohomogeneity one manifolds
Manuel Amann

Augsburg University
Terça-feira, 11 de fevereiro de 2020, 15:30
Sala 236

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.