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arXiv · 0711.1396

Novikov-symplectic cohomology and exact Lagrangian embeddings

Alexander F. Ritter
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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 π_2(L) in π_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 π_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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Alexander F. Ritter. 2009-01-12. Novikov-symplectic cohomology and exact Lagrangian embeddings. https://doi.org/10.2140/gt.2009.13.943

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