Spectral diameter of negatively monotone manifolds

Abstract

For a closed negatively monotone symplectic manifold, we construct quasi-isometric embeddings from the Euclidean spaces to its Hamiltonian diffeomorphism group, assuming it contains an incompressible heavy Lagrangian. We also show the super-heaviness of its skeleton with respect to a Donaldson hypersurface.

Expanded explanations and small correction; accepted for Journal of Symplectic Geometry