Intersections of real and quaternionic flag manifolds in complex flag manifolds, and their sum of Betti numbers

Source abstract

We show that the sum of Betti numbers of the intersections of two real flag manifolds in a complex flag manifold consisting of sequences of complex subspaces in a complex vector space are invariants of such real flag manifolds. We also show that similar claims hold for the intersections of two quaternionic flag manifolds and the intersections of real and quaternionic flag manifolds.