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Let L be an exact Lagrangian submanifold inside the cotangent bundle of aclosed manifold N. We prove that if N satisfies a mild homotopy assumption thenthe 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 orientabilityassumptions. The homotopy assumption is either that N is simply connected, ormore generally that \pi_m(N) is finitely generated for each m \geq 2.  The result is proved by constructing the Novikov homology theory forsymplectic cohomology and generalizing Viterbo's construction of a transfer mapbetween the homologies of the free loopspaces of N and L.

Novikov-symplectic cohomology and exact Lagrangian embeddings