Topology of the Fiber Product of Self-Indexing Morse Functions

. Let M and N be even dimensional connected closed manifolds. For self-indexing Morse functions f : M -* R and g : N -* R, we denote by C(f, g) the fiber product of f and g. The purpose of this paper is twofold: firstly, we prove a formula which describes chi(C(f, g)), where chi denotes the Euler characteristic. Using the formula, we compute chi(C(f, g)) for various f and g. Secondly, we compute H & lowast;(C(f, g); Z) when M and N are connected closed surfaces.