On a generalization of the abstract Morse complex and its applications
Suk Ho Hong · Nagoya Mathematical Journal · 1984
Klingenberg refers in [4] the fact that the homology group of the spaceΛof closedH1curves 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 spaceXwith an action of Lie groupGand an invariant energy functionEonX. The case of the spaceΛof closed curves is obviously obtained throughG=S1.