Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.10503 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912761157517312 |
|---|---|
| author | Wang, Zhijing Wendy |
| author_facet | Wang, Zhijing Wendy |
| contents | This paper establishes robust obstructions to representing Hamiltonian diffeomorphisms as $k$-th powers ($k \geq 2$) or embedding them in flows for certain higher-dimensional symplectic manifolds $(M,ω)$, including surface bundles. We prove that in the Hamiltonian group $(\mathrm{Ham}(M,ω), d_H)$ equipped with the Hofer metric, there exist arbitrarily large balls that are disjoint from the set of $k$-th powers. Furthermore, we demonstrate that the free group on two generators embeds into every asymptotic cone of $(\mathrm{Ham}(M,ω), d_H)$, revealing the large-scale geometric complexity of the Hamiltonian group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10503 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complexity of Hofer's geometry in higher dimensional manifolds Wang, Zhijing Wendy Symplectic Geometry Dynamical Systems 53D05, 37J65 This paper establishes robust obstructions to representing Hamiltonian diffeomorphisms as $k$-th powers ($k \geq 2$) or embedding them in flows for certain higher-dimensional symplectic manifolds $(M,ω)$, including surface bundles. We prove that in the Hamiltonian group $(\mathrm{Ham}(M,ω), d_H)$ equipped with the Hofer metric, there exist arbitrarily large balls that are disjoint from the set of $k$-th powers. Furthermore, we demonstrate that the free group on two generators embeds into every asymptotic cone of $(\mathrm{Ham}(M,ω), d_H)$, revealing the large-scale geometric complexity of the Hamiltonian group. |
| title | Complexity of Hofer's geometry in higher dimensional manifolds |
| topic | Symplectic Geometry Dynamical Systems 53D05, 37J65 |
| url | https://arxiv.org/abs/2512.10503 |