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Poisson brackets and symplectic invariants

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Abstract

We introduce new invariants associated with collections of compact subsets of a symplectic manifold. They are defined through an elementary-looking variational problem involving Poisson brackets. The proof of the non-triviality of these invariants involves various flavors of Floer theory, including the μ 3-operation in Donaldson-Fukaya category. We present applications to approximation theory on symplectic manifolds and to Hamiltonian dynamics.

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Authors and Affiliations

  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    Lev Buhovsky & Leonid Polterovich

  2. Department of Mathematics, Technion—Israel Institute of Technology, Haifa, 32000, Israel

    Michael Entov

  3. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, 69978, Israel

    Leonid Polterovich

Authors
  1. Lev Buhovsky
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  2. Michael Entov
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  3. Leonid Polterovich
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Corresponding author

Correspondence to Michael Entov.

Additional information

Lev Buhovsky—also uses the spelling “Buhovski” for his family name.

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Buhovsky, L., Entov, M. & Polterovich, L. Poisson brackets and symplectic invariants. Sel. Math. New Ser. 18, 89–157 (2012). https://doi.org/10.1007/s00029-011-0068-9

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  • DOI: https://doi.org/10.1007/s00029-011-0068-9

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