Lagrangian intersections and the Serre spectral sequence

• 成果类型: Article
• 署名作者: Barraud, Jean-Francois; Cornea, Octav
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2007.166.657
• 发表日期: 2007
• 页码: 657-722
• 关键词: homotopical dynamics; morse-theory; arnold conjecture; hamiltonian flows; geometry; INVARIANTS; HOMOLOGY

摘要

For a transversal pair of closed Lagrangian submanifolds L, L ' of a symplectic manifold M such that pi(1), (L) = pi(1) (L ') = 0 = C-1 vertical bar pi(2(M)) = omega vertical bar(pi 2(M)) and for a generic almost complex structure J, we construct an invariant with a high homotopical content which consists in the pages of order >= 2 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, we show that the pages of the spectral sequence coincide (up to a horizontal translation) with the terms of the Serre spectral sequence of the path-loop fibration Omega L -> PL -> L and we deduce some applications.