Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

Abstract

Given a symplectic surface $(\Sigma ,\omega )$ of genus $g\ge 4$, we show that the free group with two generators embeds into every asymptotic cone of $(\mathrm{Ham}(\Sigma ,\omega ),d_{\mathrm{H}})$, where $d_{\mathrm{H}}$ is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.

32 pages, 5 figures

References in corpus (1)

• Quelques plats pour la métrique de Hofer

Cited by in corpus (2)

• Bounds on spectral norms and barcodes
• Approximation of Generating Function Barcode for Hamiltonian Diffeomorphisms