Novikov-symplectic cohomology and exact Lagrangian embeddings

Details Novikov-symplectic cohomology and exact Lagrangian embeddings Novikov-symplectic cohomology and exact Lagrangian embeddings

2007-11-09

arxiv.org/abs/0711.1396v2

Geometry & Topology 13 (2009) 943-978

Mathematics

Symplectic Geometry

27 pages; added two new sections (non-simply connected cotangent bundles, unorientable setup). The final version is published

Scientific paper

10.2140/gt.2009.13.943

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.

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