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Universität Augsburg
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Universität Augsburg
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Dr. Johannes Meyer
Universität Köln
spricht am
Montag, 8. Mai 2017
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| For an (isometric Lie group) action or a (riemannian, i.e. locally equidistant) foliation in a riemannian manifold to be polar means having a global system of submanifolds that are everywhere orthogonal to the orbits or leaves respectively. In 2012 Fang, Grove and Thorbergsson showed that any positively curved, simply connected compact manifold with a polar action of cohomogeneity at least two is equivariantly diffeomorphic to a symmetric space of rank one with a polar action. Orbit decompositions of isometric actions are examples of riemannian foliations if one admits for foliations to have leaves of different dimensions. Leaves of lower dimension than the maximal one are called singular and in fact, their occurence turns out to be enforced by positive curvature. Studying their neighbourhoods is an important tool in trying to generalise the 2012 result from actions to foliations. This basically amounts to „forgetting“ the algebraic structure of the action and working only with the geometry given by ist orbit decomposition, locally recovering the algebraic structure from the geometry. In the course of this Tits geometry will play an important part: The geometry of the foliation decomposes the manifold into a cell complex and Tits‘ theory of buildings (together with a result by Burns and Spatzier) allows us to (re)construct from this the algebraic structure in some way and to obtain a suitable symmetric space. More direct geometric methods can be applied in a subcase and will be presented if time permits. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Bernhard Hanke |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).