Stability of the braid types defined by the symplecticmorphisms preserving a link
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909065569894400 |
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| author | Chen, Guanheng |
| author_facet | Chen, Guanheng |
| contents | Fix a suitable link on the disk. Recently, F. Morabito associates each Hamiltonian symplecticmorphism preserving the link to a braid type. Based on this construction, Morabito defines a family of pseudometrics on the braid groups by using the Hofer metric. In this paper, we show that two Hamiltonian symplecticmorphisms define the same braid type provided that their Hofer distance is sufficiently small. As a corollary, the pseudometric defined by Morabito is nondegenerate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03845 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability of the braid types defined by the symplecticmorphisms preserving a link Chen, Guanheng Symplectic Geometry Geometric Topology Fix a suitable link on the disk. Recently, F. Morabito associates each Hamiltonian symplecticmorphism preserving the link to a braid type. Based on this construction, Morabito defines a family of pseudometrics on the braid groups by using the Hofer metric. In this paper, we show that two Hamiltonian symplecticmorphisms define the same braid type provided that their Hofer distance is sufficiently small. As a corollary, the pseudometric defined by Morabito is nondegenerate. |
| title | Stability of the braid types defined by the symplecticmorphisms preserving a link |
| topic | Symplectic Geometry Geometric Topology |
| url | https://arxiv.org/abs/2309.03845 |