On a result concerning a property of closed manifolds (Q2711487)

Let \(M\) be a closed smooth manifold, and let \(\gamma(M)\) be the minimal number of critical points of Morse functions on \textit{M. G. M. Rassias} [Tamkang J. Math. 10, 67-73 (1979; Zbl 0442.57013)] proved that, for every \(k\)-fold covering \(\widetilde M \to M\), \(\gamma(\tilde M) \leq k\gamma(M)-4(k-1)\). The author proves that this inequality is in fact an equality provided that \(M\) is a closed surface (because in this case \(\gamma(M)=4-\chi(M)\)).