On the cohomology of some exceptional symmetric spaces

Abstract

This is a survey on the construction of a canonical or "octonionic Kähler" 8-form, representing one of the generators of the cohomology of the four Cayley-Rosenfeld projective planes. The construction, in terms of the associated even Clifford structures, draws a parallel with that of the quaternion Kähler 4-form. We point out how these notions allow to describe the primitive Betti numbers with respect to different even Clifford structures, on most of the exceptional symmetric spaces of compact type.

arXiv comment12 pages. Proc. INdAM Workshop "New Perspectives in Differential Geometry" held in Rome, Nov. 2015, to appear in Springer-INdAM Series