The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians - Yasuhiko Kamiyama (International Journal of Mathematics and Mathematical Sciences)
For F=R, C, or H, let GkFn denote the Grassmannian of k-planes in Fn. For a well-known Morse function f:GkFn⟶R, we denote by Cf the fiber product of two copies of f. We prove a formula which describes χCf.