Seminar for Combinatorics, Geometry, Algebra and Topology
Seminar Kombinatorika, Geometrija, Topologija, Algebra (KGTA)
Plan rada za septembar 2016:
Utorak, 20.09.2016. u 12:00, soba 301f, MI SANU:
Marcus Zibrowius, Heinrich Heine University Düsseldorf, Germany
HOMOGENEOUS BUNDLES ON HOMOGENEOUS SPACES
Abstract: Consider a compact homogeneous manifold of the form G/H, where G is a compact Lie group and H a subgroup of maximal rank. A classical theorem of Atiyah, Hirzebruch, Hodgkin and Pittie asserts that, under mild hypotheses, every complex vector bundle on G/H is “stably homogeneous”, i.e. arises from some complex representation of H. Is the same true for real vector bundles and real representations? The situation is in fact still unclear. I will outline a (mostly) negative answer for “full flag varieties” (G/T with T a maximal torus), but also mention some recent positive results for homogeneous spaces of positive curvature.
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