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