Morse inequalities for \({\mathbb{R}{}}\)-constructible sheaves
It is well known that there is a relation between the topology of a compact manifold and the critical points of any real valued function. This relation is described in terms of a collection of inequalities, the Morse-Bott inequalities, involving Betti numbers and the number of critical points of a given index. In this paper the authors give a generalization for \(\mathbb{R}\)-constructible sheaves of these inequalities showing the relation between Morse theory and microlocal analysis of sheaves. The paper is strongly based on \textit{M. Kashiwara} [Astérisque 130, 193-209 (1985; Zbl 0568.32017)] and \textit{M. Kashiwara} and \textit{P. Schapira} [Microlocal study of sheaves (Astérisque 128) (1985; Zbl 0589.32019)]. A book on the subject is the following: \textit{M. Kashiwara} and \textit{P. Schapira} [Sheaves on manifolds (Grundlehren der Mathematischen Wissenschaften, 292, Springer-Verlag, Berlin) (1990; Zbl 0709.18001)].
scientific article; zbMATH DE number 62677
scientific article