November 27, 2006
Rémi Leclercq (Montreal): Spectral invariants in Lagrangian intersection theory
Abstract:
Let $(M,\omega)$ be a symplectic manifold compact or convex at
infinity. Consider a closed Lagrangian submanifold $L$ such that the
symplectic form and the Maslov index vanish on $\pi_2(M,L)$. Given any
Lagrangian submanifold $L'$, Hamiltonian isotopic to $L$, we define
Lagrangian spectral invariants associated to the non zero homology
classes of $L$, depending on $L$ and $L'$. We show that they naturally
generalize the Hamiltonian spectral invariants introduced by Oh and
Schwarz. We provide a way to distinguish them one from another and
estimate their difference in terms of a geometric quantity. Finally, we
show that they are the homological counterparts of higher order
invariants, which we define via spectral sequence machinery introduced
by Barraud and Cornea.
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