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Morse theory for Lagrangian intersections
Soit P une variete symplectique compacte et soit L⊂P une sous-variete lagrangienne avec π 2 (P,L)=0. Pour un diffeomorphisme exact φ de P avec la propriete que φ(L) coupe L transversalement, on
An instanton-invariant for 3-manifolds
To an oriented closed 3-dimensional manifoldM withH1(M, ℤ)=0, we assign a ℤ8-graded homology groupI*(M) whose Euler characteristic is twice Casson's invariant. The definition uses a construction on
Symplectic fixed points and holomorphic spheres
LetP be a symplectic manifold whose symplectic form, integrated over the spheres inP, is proportional to its first Chern class. On the loop space ofP, we consider the variational theory of the
The unregularized gradient flow of the symplectic action
The symplectic action can be defined on the space of smooth paths in a symplectic manifold P which join two Lagrangian submanifolds of P. To pursue a new approach to the variational theory of this
Transversality in elliptic Morse theory for the symplectic action
Our goal in this paper is to settle some transversality question for the perturbed nonlinear Cauchy-Riemann equations on the cylinder. These results play a central role in the denition of symplectic
We investigate the relation between the trajectories of a finite dimensional gradient flow connecting two critical points and the cohomology of the surrounding space. The results are applied to an