Disjoint superheavy subsets and fragmentation norms

概要

We present a lower bound for a fragmentation norm and construct a bi-Lipschitz embedding $I:{\mathbb{R}}^n\to \mathrm{Ham}(M)$ with respect to the fragmentation norm on the group $\mathrm{Ham}(M)$ of Hamiltonian diffeomorphisms of a symplectic manifold $(M,\omega )$. As an application, we provide an answer to Brandenbursky’s question on fragmentation norms on $\mathrm{Ham}({\mathrm{\Sigma }}_g)$, where ${\mathrm{\Sigma }}_g$ is a closed Riemannian surface of genus $g\ge 2$.