Abstract
Given a symplectic surface (σ,ω) of genus g ≥ 4, we show that the free group with two generators embeds into every asymptotic cone of (Ham(σ,ω),dH), where dH is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.
Original language | English (US) |
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Pages (from-to) | 467-498 |
Number of pages | 32 |
Journal | Journal of Topology and Analysis |
Volume | 11 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1 2019 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Geometry and Topology
Keywords
- Hamiltonian diffeomorphisms
- Hofer's metric
- asymptotic cones
- egg beater map
- embeddings of free groups