On Gromov Width under $C^0$ Deformations
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912484299898880 |
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| author | Cattalani, Spencer |
| author_facet | Cattalani, Spencer |
| contents | We construct a uniformly bounded symplectic structure on $S^2 \times \mathbb{R}^4$ admitting embeddings by arbitrarily large balls. This provides a counterexample to a recent conjecture of Savelyev. We then prove the conjecture holds for a wide class of examples, generalizing a result by Savelyev. Along the way, we clarify some aspects of pseudoholomorphic curve theory in non-compact manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11466 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Gromov Width under $C^0$ Deformations Cattalani, Spencer Symplectic Geometry 32Q65, 32Q60, 53D05 We construct a uniformly bounded symplectic structure on $S^2 \times \mathbb{R}^4$ admitting embeddings by arbitrarily large balls. This provides a counterexample to a recent conjecture of Savelyev. We then prove the conjecture holds for a wide class of examples, generalizing a result by Savelyev. Along the way, we clarify some aspects of pseudoholomorphic curve theory in non-compact manifolds. |
| title | On Gromov Width under $C^0$ Deformations |
| topic | Symplectic Geometry 32Q65, 32Q60, 53D05 |
| url | https://arxiv.org/abs/2507.11466 |