  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.
