Intersection Theory for Lagrangian Immersions

We introduce Floer homology for transversely intersecting Lagrangian immersions $L$ and $L'$ in a symplectic manifold $(X,\omega )$. By using this homology, if $\pi _2(X,L)=0$ and $L'$ is the image of $L$ under a Hamiltonian isotopy, then the number of the intersection points of $L$ and $L'$ is bounded below by the sum of the ${\bf Z}_2$-betti numbers of $L$ (or rather, the manifold whose immersion is $L$) and a non-negative extra term coming from the self-intersections of $L$.

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Published 1 January 2005