Geometrical Decomposition of the Free Loop Space on a Manifold with Finitely Many Closed Geodesics |
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Authors: | Morgenstern Thomas |
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Institution: | (1) Mathematisches Institut der Universität Heidelberg, Im Neuenheimer Feld 288, 69122 Heidelberg, Germany |
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Abstract: | In Morse theory an isolated degenerate critical point can be resolved into a finite number of nondegenerate critical points by perturbing the totally degenerate part of the Morse function inside the domain of a generalized Morse chart. Up to homotopy we can admit pertubations within the whole characteristic manifold. Up to homotopy type a relative CW-complex is attached, which is the product of a big relative CW-complex, representing the degenerate part, and a small cell having the dimension of the Morse index. |
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Keywords: | Morse theory closed geodesics critical points free loop space Lusternik– Schnirelmann category |
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