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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1097347-0
PII: S 0002-9939(1992)1097347-0
Article copyright: © Copyright 1992 American Mathematical Society