Lagrangian intersections

For a transversal pair of closed Lagrangian submanifolds L, L of a symplectic manifold M such that π1 (L) = π1 (L ) = 0 = c1 |π2 (M ) = ω|π2 (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...

67p noel_noel 17-01-2013 59 6   Download

Characteristic classes for oriented pseudomanifolds can be defined using appropriate self-dual complexes of sheaves. On non-Witt spaces, self-dual complexes compatible to intersection homology are determined by choices of Lagrangian structures at the strata of odd codimension. We prove that the associated signature and L-classes are independent of the choice of Lagrangian structures, so that singular spaces with odd codimensional strata, such as e.g. certain compactifications of locally symmetric spaces, have well-defined L-classes, provided Lagrangian structures exist.

25p noel_noel 17-01-2013 54 7   Download