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On the Floer homology of cotangent bundles

✍ Scribed by Alberto Abbondandolo; Matthias Schwarz

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
471 KB
Volume
59
Category
Article
ISSN
0010-3640

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✦ Synopsis

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 W 1,2 free or based loops on M.

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