Homotopy type of path spaces

Author:
Diane Kalish

Journal:
Proc. Amer. Math. Soc. **116** (1992), 259-271

MSC:
Primary 58B05; Secondary 55P99, 58E05, 58E10

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

MathSciNet review:
1097347

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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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DOI:
https://doi.org/10.1090/S0002-9939-1992-1097347-0

Article copyright:
© Copyright 1992
American Mathematical Society