Complex and oriented Grassmannians of planes and their quotients by maximal compact tori

Dr Hendrik Süß (University of Manchester)

Frank Adams Room 1,

Victor Buchstaber and Svjetlana Terzić showed that the quotient of the complex Grassmannian G(2,4) by the natural action of the compact 4-torus is a topological sphere. Interestingly G(2,4) coincides with the Grassmannian of oriented planes in R^6. This observation offers two possible direction to generalise the result of Buchstaber and Terzić. Either to higher dimensional complex or to higher dimensional oriented Grassmannians. I am going to discuss why the first generalisation is much harder to achieve than the second. On the way I will touch some useful concepts from algebraic and symplectic Geometry.

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