THE ELIMINATION OF CRITICAL POINTS OF A NON-DEGENERATE FUNCTION ON A DIFFERENTIABLE MANIFOLD,
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 26, 1964
- Accession Number
- AD0617854
Entities
People
- Marston Morse
Organizations
- Institute for Advanced Study