On the Floer homology of cotangent bundles |
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Authors: | Alberto Abbondandolo Matthias Schwarz |
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Institution: | 1. Scuola Normale Superiore di PisaDipartimento di Matematica, Università di Pisa, via Buonarroti 2, 56127 Pisa, Italy;2. Mathematisches Institut, Universit?t Leipzig, Augustusplatz 10/11, PF 920, D‐04109 Leipzig, Germany |
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Abstract: | This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T* M of a compact orientable manifold M. The first result is a new L∞ estimate for the solutions of the Floer equation, which allows us to deal with a larger—and more natural—class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Floer homology and the singular homology of the free loop space of M in the periodic case, or of the based loop space of M in the Lagrangian intersection problem. The idea for the construction of such an isomorphism is to consider a Hamiltonian that is the Legendre transform of a Lagrangian on T M and to construct an isomorphism between the Floer complex and the Morse complex of the classical Lagrangian action functional on the space of W1,2 free or based loops on M. © 2005 Wiley Periodicals, Inc. |
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