Exact Lagrangian submanifolds in simply-connected cotangent bundles
Symplectic Geometry
2009-11-13 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/0701783,
title = {Exact Lagrangian submanifolds in simply-connected cotangent bundles},
author = {Kenji Fukaya and Paul Seidel and Ivan Smith},
journal= {arXiv preprint arXiv:math/0701783},
year = {2009}
}
Comments
28 pages, 3 figures. Version 2 -- derivation and discussion of the spectral sequence considerably expanded. Other minor changes