English

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