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Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces
Linus Kramer
We classify compact 2-connected homogeneous spaces with the same rational cohomology as a product of spheres. This classification relies on spectral sequences, homotopy theory, and…
Loop groups and twin buildings
Linus Kramer
We describe some buildings related to complex Kac-Moody groups. First we describe the spherical building of SLn(C) (i.e. the projective geometry PG(Cn)) and its Veronese representa…
Two-transitive Lie groups
Linus Kramer
Using a characterization of parabolics in reductive Lie groups due to Furstenberg, elementary properties of buildings, and some algebraic topology, we give a new proof of Tits' cla…
Compact Polygons
Linus Kramer
We develop the basic topological properties of compact polygons, i.e. of compact topological Tits buildings of rank two. It is proved that the Coxeter diagram of such a building is…