Title :

Lagrangian Intersections and the Serre Spectral Sequence

Author(s) :

Barraud, J. F. [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Cornea, O. [Auteur]

HAL domain(s) :

Mathématiques [math]/Géométrie différentielle [math.DG]
Mathématiques [math]/Géométrie symplectique [math.SG]

English abstract : [en]

For a transversal pair of closed Lagrangian submanifolds $L, L'$ of a symplectic manifold $M$ so that $\pi_{1}(L)=\pi_{1}(L')=0=c_{1}|_{\pi_{2}(M)}=\omega|_{\pi_{2}(M)}$ and a generic almost complex structure $J$ we construct ...
Show more >For a transversal pair of closed Lagrangian submanifolds $L, L'$ of a symplectic manifold $M$ so that $\pi_{1}(L)=\pi_{1}(L')=0=c_{1}|_{\pi_{2}(M)}=\omega|_{\pi_{2}(M)}$ and a generic almost complex structure $J$ we construct an invariant with a high homotopical content which consists in the pages of order $\geq 2$ 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, these pages coincide (up to a horizontal translation) with the terms of the Serre-spectral sequence of the path-loop fibration $\Omega L\to PL\to L$. Among other applications we prove that, in this case, each point $x\in L\backslash L'$ belongs to some pseudo-holomorpic strip of symplectic area less than the Hofer distance between $L$ and $L'$.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL