Abstract:This paper extends the Fundamental Theorem of Morse Theory to the two endmanifold case. The theorem relates the homotopy type of the space of paths connecting two submanifolds of a Riemannian manifold to the critical points of the energy function defined on this path space. Use of the author’s formulation of the Morse index Theorem in this setting allows for a simple computation of the homotopy type, and several specific examples are worked out.
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- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 259-271
- MSC: Primary 58B05; Secondary 55P99, 58E05, 58E10
- DOI: https://doi.org/10.1090/S0002-9939-1992-1097347-0
- MathSciNet review: 1097347