Reduction of symplectic homeomorphisms

Abstract

In a previous article, we proved that symplectic homeomorphisms preserving a coisotropic submanifold C, preserve its characteristic foliation as well. As a consequence, such symplectic homeomorphisms descend to the reduction of the coisotropic C. In this article we show that these reduced homeomorphisms continue to exhibit certain symplectic properties. In particular, in the specific setting where the symplectic manifold is a torus and the coisotropic is a standard subtorus, we prove that the reduced homeomorphism preserves spectral invariants and hence the spectral capacity. To prove our main result, we use Lagrangian Floer theory to construct a new class of spectral invariants which satisfy a non-standard triangle inequality.

39 pages, to appear in Annales scientifiques de l'École normale supérieure

References in corpus (2)

• Some quantitative results in $C^0$ symplectic geometry
• $C^0$-rigidity of characteristics in symplectic geometry

Cited by in corpus (6)

• The action spectrum and C^0 symplectic topology
• A C^0 counterexample to the Arnold conjecture
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• On the supports in the Humilière completion and $\gamma$-coisotropic sets
• Piunikhin-Salamon-Schwarz isomorphisms and spectral invariants for conormal bundle
• Dehn-Seidel twist, $C^0$ symplectic topology and barcodes