  We prove that any closed connected exact Lagrangian manifold L in a connected
cotangent bundle T*N is up to a finite covering space lift a homology
equivalence. We prove this by constructing a fibrant parametrized family of
ring spectra FL parametrized by the manifold N. The homology of FL will be
(twisted) symplectic cohomology of T*L. The fibrancy property will imply that
there is a Serre spectral sequence converging to the homology of FL and the
product combined with intersection product on N induces a product on this
spectral sequence. This product structure and its relation to the intersection
product on L is then used to obtain the result. Combining this result with work
of Abouzaid we arrive at the conclusion that L -> N is always a homotopy
equivalence.
