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 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.

27 pages; added two new sections (non-simply connected cotangent bundles, unorientable setup). The final version is published in Geometry & Topology 13, 2009

References in corpus (4)

• Functors and Computations in Floer homology with Applications Part II
• Floer homology and the heat flow
• Exact Lagrangian submanifolds in simply-connected cotangent bundles
• Microlocal branes are constructible sheaves

Cited by in corpus (14)

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• Floer theory for negative line bundles via Gromov-Witten invariants
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• Deformed Hamiltonian Floer theory, capacity estimates, and Calabi quasimorphisms
• Circle-actions, quantum cohomology, and the Fukaya category of Fano toric varieties
• Local systems on the free loop space and finiteness of the Hofer-Zehnder capacity
• Hamiltonian Floer homology for compact convex symplectic manifolds
• Homotopy type of the unitary group of the uniform Roe algebra on ${\mathbb{Z}}^n$
• Quantum Steenrod squares and the equivariant pair-of-pants in symplectic cohomology
• Invariance of symplectic cohomology and twisted cotangent bundles over surfaces
• Lagrangian Cobordisms in Liouville manifolds
• The role of the Legendre transform in the study of the Floer complex of cotangent bundles
• The spectral diameter of a Liouville domain