Abstract
Let Mn be a compact, connected topological manifold and F a continuous mapping of Mn into R that is “topologically nondegenerate” in the sense of (Morse, M. (1959) J. d'Analyse Math., 7, 189-208). Let c be a value of F and set Fc = {p∈Mn|F(p) ≤ c}. The topological critical points of F on Fc are finite in number and can be related to the invariants of the homology groups of Fc as in the differentiable case. F-Deformations and F-tractions make this possible. F-Tractions are here defined and replace retracting deformations used in the differentiable case. The final relations will serve as a model for similar relations between critical extremals of Weierstrass integrals on Riemannian manifolds.
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