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Maximum principles in symplectic homology

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Abstract

In the setting of symplectic manifolds which are convex at infinity, we use a version of the Aleksandrov maximum principle to derive uniform estimates for Floer solutions that are valid for a wider class of Hamiltonians and almost complex structures than is usually considered. This allows us to extend the class of Hamiltonians which one can use in the direct limit when constructing symplectic homology. As an application, we detect elements of infinite order in the symplectic mapping class group of a Liouville domain and prove existence results for translated points.

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Authors and Affiliations

  1. Department of Mathematics, ETH Zürich, HG J 56, 8092, Zürich, Switzerland

    Will J. Merry

  2. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000, Belgrade, Serbia

    Igor Uljarevic

Authors
  1. Will J. Merry
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  2. Igor Uljarevic
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Correspondence to Will J. Merry.

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Merry, W.J., Uljarevic, I. Maximum principles in symplectic homology. Isr. J. Math. 229, 39–65 (2019). https://doi.org/10.1007/s11856-018-1792-z

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  • DOI: https://doi.org/10.1007/s11856-018-1792-z

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