Morse inequalities for almost-periodic functions (Q1178091)

Let \(\tilde X\) be a finite dimensional manifold on which a group \(\Gamma\cong Z^ l\) acts freely such that \(X=\tilde X/\Gamma\) be a compact manifold. The author shows that, in some sense, any almost periodic function on \(\tilde X\) satisfying suitable regularity conditions admits uniquely a mean \(\bar m_ p\) for its critical points of index \(p\). Then he proves that there are satisfied Morse-type inequalities relating the quantities \(\bar m_ p\) to the Betti numbers \(\bar b_ p\) associated with the covering \(\tilde X\to X\).