Morse inequalities for R-constructible sheaves

✍ Scribed by P Schapira; N Tose

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 279 KB
• Volume: 93
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1016/0001-8708(92)90022-d

✦ Synopsis

This note aims at generalizing of classical Morse inequalities for Betti numbers of compact manifolds (cf. [lo, 1,2]). In this paper, we work with R-constructible sheaves instead and encounter the tight relation between Morse theory and microlocal analysis of sheaves. See Witten [ 111, HellTer and Sjiistrand [S, 61, and Henniart [7] for another approach to Morse inequalities via microlocal analysis and also Goresky and MacPherson [3,4] who introduced the "stratified Morse theory". This paper may be considered as a variation on Kashiwara's index theorem [8], and in fact our proof is a slight modification of his.

If V~ob(@(Mod~(k))), we set b,(V)=dimH'(V) (and we define b:(V) and x(V) = bz( V) as in (1.1)).