Accession Number:

AD0617854

Title:

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

Descriptive Note:

Corporate Author:

INSTITUTE FOR ADVANCED STUDY PRINCETON N J

Personal Author(s):

Report Date:

1964-05-26

Pagination or Media Count:

65.0

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

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE