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On a generalization of the abstract Morse complex and its applications

Published online by Cambridge University Press:  22 January 2016

Suk Ho Hong
Suk Ho Hong*
Affiliation:
Department of Mathematics, Nagoya University, Nagoya 464 Japan
*
Department of Mathematics, Kon-huh, University Seoul, Korea
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Klingenberg refers in [4] the fact that the homology group of the space Λ of closed H1 curves on a manifold is isomorphic to that of the Morse complex. In this paper, we generalize the fact above and at the same time give a proof to it through cell decomposition method under a strong non degeneracy condition.

We first introduce so-called generalized Morse complex on a space X with an action of Lie group G and an invariant energy function E on X. The case of the space Λ of closed curves is obviously obtained through G = S1.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 96 , December 1984 , pp. 71 - 82
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

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