Connectivities Ri of Fréchet Spaces in Variational Topology

AUTOR(ES)

Morse, Marston

RESUMO

A global study of geodesics, joining points A1 [unk] A2 on a Riemannian manifold Nn, is oriented by the answers given to two questions. How does the concept of a nondegenerate geodesic enter, and what topological invariants best condition the geodesics joining A1 to A2? We answer the first question by defining and exploiting nondegenerate point pairs A1 [unk] A2 on Nn. The connectivities Ri of Mn used in ordinary critical point theory should be replaced by the connectivities Ri of the pathwise components of the Fréchet metric space [unk]A1A2 defined in this paper. These components are homeomorphic. Their connectivities Ri condition the geodesics joining A1 to A2 on Nn in a way to be disclosed. Detailed proofs are found in the references listed, or will be presented later.

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