Morse inequalities for \({\mathbb{R}{}}\)-constructible sheaves
type: Item
instance of: scholarly article
title: Morse inequalities for \({\mathbb{R}{}}\)-constructible sheaves
zbMATH Open document ID: 0767.58008
DOI: 10.1016/0001-8708(92)90022-D
author: Pierre Schapira
author: N. Tose
published in: Advances in Mathematics
publication date: 1992-09-27T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 58E05
Mathematics Subject Classification ID: 58J15
zbMATH DE Number: 62677
zbMATH Keywords: \(\mathbb{R}\)-constructible sheaves
zbMATH Keywords: microlocal analysis of sheaves
reviewed by: Juan Monterde
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 62677