Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Homotopy type of path spaces
HTML articles powered by AMS MathViewer

by Diane Kalish PDF
Proc. Amer. Math. Soc. 116 (1992), 259-271 Request permission

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.
References
Similar Articles
Additional Information
  • © 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