Lagrangian Intersections and the Serre Spectral Sequence
Abstract
For a transversal pair of closed Lagrangian submanifolds L, L' of a symplectic manifold M so that and a generic almost complex structure J we construct an invariant with a high homotopical content which consists in the pages of order of a spectral sequence whose differentials provide an algebraic measure of the high-dimensional moduli spaces of pseudo-holomorpic strips of finite energy that join L and L'. When L and L' are hamiltonian isotopic, these pages coincide (up to a horizontal translation) with the terms of the Serre-spectral sequence of the path-loop fibration . Among other applications we prove that, in this case, each point belongs to some pseudo-holomorpic strip of symplectic area less than the Hofer distance between L and L'.
Cite
@article{arxiv.math/0401094,
title = {Lagrangian Intersections and the Serre Spectral Sequence},
author = {J. F. Barraud and O. Cornea},
journal= {arXiv preprint arXiv:math/0401094},
year = {2007}
}
Comments
55 pages. LaTeX. fixed some imprecisions in the appendix