The Witten complex and the degenerate Morse inequalities
\textit{E. Witten} [ibid. 17, 661-692 (1982; Zbl 0499.53056)] presented an analytic proof of the nondegenerate Morse inequalities, and suggested a method of proof of the degenerate Morse inequalities of Bott when the function has non-degenerate critical submanifolds. In this paper, the author uses the complex introduced by Witten, and gives a rigorous probabilistic proof of these inequalities. The method is based on an extension of the heat equation method for the proof of the index theorem by the author [J. Funct. Anal. 57, 56-99 (1984; Zbl 0538.58033)]. However, in the proof of the Morse inequalities of Bott, the Mayer- Vietoris argument is used. This question has recently received a complete analytical solution by \textit{B. Helffer} and \textit{J. Sjöstrand} [Commun. Partial Differ. Equations 10, 245-340 (1985; Zbl 0597.35024)] and 'A proof of the Bott inequalities', to appear in a volume in the honor of M. Sato.
scientific article; zbMATH DE number 3984180