Exact Lagrangian submanifolds in simply-connected cotangent bundles

Details Exact Lagrangian submanifolds in simply-connected cotangent bundles Exact Lagrangian submanifolds in simply-connected cotangent bundles

2007-01-26

arxiv.org/abs/math/0701783v2

Mathematics

Symplectic Geometry

28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor change

Scientific paper

10.1007/s00222-007-0092-8

We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel-Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler, using a different approach.

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