Novikov-symplectic cohomology and exact Lagrangian embeddings
Abstract
Let L be an exact Lagrangian submanifold inside the cotangent bundle of a closed manifold N. We prove that if N satisfies a mild homotopy assumption then the image of \pi_2(L) in \pi_2(N) has finite index. We make no assumption on the Maslov class of L, and we make no orientability assumptions. The homotopy assumption is either that N is simply connected, or more generally that \pi_m(N) is finitely generated for each m \geq 2. The result is proved by constructing the Novikov homology theory for symplectic cohomology and generalizing Viterbo's construction of a transfer map between the homologies of the free loopspaces of N and L.
Keywords
Cite
@article{arxiv.0711.1396,
title = {Novikov-symplectic cohomology and exact Lagrangian embeddings},
author = {Alexander F. Ritter},
journal= {arXiv preprint arXiv:0711.1396},
year = {2014}
}
Comments
27 pages; added two new sections (non-simply connected cotangent bundles, unorientable setup). The final version is published in Geometry & Topology 13, 2009