Details

Autor(en) / Beteiligte

• Abbondandolo, Alberto
• Schwarz, Matthias

Titel

On the Floer homology of cotangent bundles

Ist Teil von

• Communications on pure and applied mathematics, 2006-02, Vol.59 (2), p.254-316

Ort / Verlag

Hoboken: Wiley Subscription Services, Inc., A Wiley Company

Erscheinungsjahr

2006

Link zum Volltext

Quelle

Wiley Online Library Journals Frontfile Complete

Beschreibungen/Notizen

• 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.