Lagrangian intersections and the Serre spectral sequence

• Autores: Jean François Barraud, Octav Cornea
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 166, Nº 3, 2007, págs. 657-722
• Idioma: inglés
• DOI: 10.4007/annals.2007.166.657
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• Resumen

  • For a transversal pair of closed Lagrangian submanifolds L,L' of a symplectic manifold M such that pi1(L) = pi1(L') = 0 = c1|pi2(M) = w|pi2(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 highdimensional 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 OL - PL - L and we deduce some applications.