Accession Number : AD0617854

Title :   THE ELIMINATION OF CRITICAL POINTS OF A NON-DEGENERATE FUNCTION ON A DIFFERENTIABLE MANIFOLD,

Corporate Author : INSTITUTE FOR ADVANCED STUDY PRINCETON N J

Personal Author(s) : Morse,Marston

Report Date : 26 MAY 1964

Pagination or Media Count : 65

Abstract : M is a compact, connected, orientable, differentiable n-manifold of class C, and f is a non-degenerate function of class C. This note reveals certain fundamental topological characteristics of M by combining the study of the critical points of f with the study of certain differentiable submanifolds of M associated with the respective critical points of f and termed bowls of f. An attempt is made to modify f so as to eliminate as many critical points as possible, replacing f by another nondegenerate function. This is accomplished mainly through the development of a theorem concerning bowls and the existence of a non-degenerate function without critical points in a given neighborhood. (Author)

Descriptors :   (*FUNCTIONS(MATHEMATICS), ALGEBRAIC TOPOLOGY), (*ALGEBRAIC TOPOLOGY, FUNCTIONS(MATHEMATICS)), DIFFERENTIAL EQUATIONS, THEORY, TOPOLOGY

Distribution Statement : APPROVED FOR PUBLIC RELEASE