Parametrized Ring-Spectra and the Nearby Lagrangian Conjecture

  title={Parametrized Ring-Spectra and the Nearby Lagrangian Conjecture},
  author={Thomas Kragh},
  journal={Geometry & Topology},
  • Thomas Kragh
  • Published 2013
  • Mathematics
  • Geometry & Topology
  • Let L be an embedded closed connected exact Lagrangian submanifold in a connected cotangent bundle T N . In this paper we prove that such an embedding is, up to a finite covering space lift of T N , 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 the (twisted) symplectic cohomology of T L. The fibrancy property will imply that there is a Serre spectral sequence converging to the… CONTINUE READING

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