Spectral diameter of negatively monotone manifolds

TL;DR

This paper explores the geometric properties of negatively monotone symplectic manifolds, constructing embeddings into their Hamiltonian diffeomorphism groups and analyzing the super-heaviness of their skeletons.

Contribution

It introduces quasi-isometric embeddings into Hamiltonian groups under specific conditions and proves super-heaviness of the skeleton with respect to Donaldson hypersurfaces.

Findings

Constructed quasi-isometric embeddings from Euclidean spaces to Hamiltonian diffeomorphism groups.

Proved super-heaviness of the skeleton with respect to Donaldson hypersurfaces.

Established conditions involving incompressible heavy Lagrangians.

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.