On the Floer homology of cotangent bundles

Details On the Floer homology of cotangent bundles On the Floer homology of cotangent bundles

2004-08-20

arxiv.org/abs/math/0408280v2

Comm. Pure Appl. Math. 59 (2006) 254-316

Mathematics

Symplectic Geometry

50 pages, added detailed proof of the invariance under homotopy (to appear in Communications in Pure and Applied Mathematics)

Scientific paper

10.1002/cpa.2009

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle of a compact orientable manifold M. The first result is a new uniform estimate for the solutions of the Floer equation, which allows 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 which is the Legendre transform of a Lagrangian on TM, and to construct an isomorphism between the Floer complex and the Morse complex of the classical Lagrangian action functional on the space of free or based loops on M of Sobolev class W(1,2).

Affiliated with

Also associated with

No associations

Rating

On the Floer homology of cotangent bundles does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Floer homology of cotangent bundles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Floer homology of cotangent bundles will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-713710