Disjoint superheavy subsets and fragmentation norms

Morimichi Kawasaki, Ryuma Orita
Journal of Topology and Analysis, vol. 13 (2021), no. 2, pp. 443–468
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Abstract

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We present a lower bound for a fragmentation norm and construct a bi-Lipschitz embedding $I\colon \mathbb{R}^n\to\mathrm{Ham}(M)$ 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 $g\geq 2$.

@article{kawasaki2021disjoint,
  author        = {Kawasaki, Morimichi and Orita, Ryuma},
  title         = {{Disjoint superheavy subsets and fragmentation norms}},
  journal       = {Journal of Topology and Analysis},
  volume        = {13},
  number        = {2},
  pages         = {443--468},
  year          = {2021},
  doi           = {10.1142/S179352532050017X},
  eprint        = {1901.01647},
  archivePrefix = {arXiv}
}