HOMOLOGY OF THE FIBER PRODUCT OF THE MORSE FUNCTION ON THE UNIT TANGENT BUNDLE OF A SPHERE

Abstract

Let $V_2\left(\mathrm{P}^{n+1}\right)$ be the Stiefel manifold of orthogonal 2-frames in $\mathrm{P}^{n+1}$. Let $f_{n+1,2}: V_2\left(\mathrm{P}^{n+1}\right) \rightarrow \mathrm{P}$ be the well-known Morse function and $C\left(f_{n+1,2}\right)$ be the fiber product of two copies of $f_{n+1,2}$. Then, we determine the homology groups $H_*\left(C\left(f_{n+1,2}\right) ; \mathrm{Z}\right)$.

Received: August 22, 2025
Accepted: September 5, 2025