Disjoint superheavy subsets and fragmentation norms

Abstract

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 $\mathrm{Ham}({\Sigma }_g)$, where ${\Sigma }_g$ is a closed Riemannian surface of genus $g\ge 2$

21 pages

References in corpus (1)

• Quasi-morphisms and quasi-states in symplectic topology