Homotopy type of path spaces

Kalish, Diane

doi:10.1090/S0002-9939-1992-1097347-0

Homotopy type of path spaces
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Proc. Amer. Math. Soc. 116 (1992), 259-271 Request permission

Erratum: Proc. Amer. Math. Soc. 118 (1993), 1015.

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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Aspects of Morse theory

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