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Exact Lagrangian submanifolds in simply-connected cotangent bundles

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We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second Stiefel–Whitney class of the Lagrangian submanifold) we prove such submanifolds are Floer-cohomologically indistinguishable from the zero-section. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler [16], using a different approach.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Kyoto University, Kyoto, 602-8502, Japan

    Kenji Fukaya

  2. MIT Department of Mathematics, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Paul Seidel

  3. Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, UK

    Ivan Smith

Authors
  1. Kenji Fukaya
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  2. Paul Seidel
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  3. Ivan Smith
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Corresponding authors

Correspondence to Kenji Fukaya or Ivan Smith.

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Fukaya, K., Seidel, P. & Smith, I. Exact Lagrangian submanifolds in simply-connected cotangent bundles. Invent. math. 172, 1–27 (2008). https://doi.org/10.1007/s00222-007-0092-8

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  • DOI: https://doi.org/10.1007/s00222-007-0092-8

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