Abstract
Let be an embedded closed connected exact Lagrangian submanifold in a connected cotangent bundle . In this paper we prove that such an embedding is, up to a finite covering space lift of , a homology equivalence. We prove this by constructing a fibrant parametrized family of ring spectra parametrized by the manifold . The homology of will be the (twisted) symplectic cohomology of . The fibrancy property will imply that there is a Serre spectral sequence converging to the homology of . The fiber-wise ring structure combined with the intersection product on induces a product on this spectral sequence. This product structure and its relation to the intersection product on is then used to obtain the result. Combining this result with work of Abouzaid we arrive at the conclusion that is always a homotopy equivalence.
Citation
Thomas Kragh. "Parametrized ring-spectra and the nearby Lagrangian conjecture." Geom. Topol. 17 (2) 639 - 731, 2013. https://doi.org/10.2140/gt.2013.17.639
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