Topological invariants for discrete group actions (Q703994)

In a previous paper, the author and \textit{M. Gromov} [Dynamical Morse entropy, in: Dynamical Morse entropy, in: Modern dynamical systems and applications. Edited by M. Briu, B. Hasselblatt and Y. Pesin. Cambridge: Cambridge University Press, 27--44 (2004)] considered a dynamical version of the classical Morse inequalities allowing degenerated critical points. Their inequality is given in terms of the category and the cup-length of the manifold. In this paper, the author explains how such an inequality is obtained via classical Morse theory, statistical mechanics and homology entropy for group actions.