Abstract
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 pseudometrics defined by Morabito are nondegenerate.
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Acknowledgements
The author would like to thank the anonymous referee for his/her detailed comments, suggestions and corrections have greatly improved this paper. The author is supported by the National Natural Science Foundation of China Youth Fund Project, Grant number: 12201106.
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Chen, G. Stability of the braid types defined by the symplecticmorphisms preserving a link. J. Fixed Point Theory Appl. 26, 8 (2024). https://doi.org/10.1007/s11784-023-01095-3
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DOI: https://doi.org/10.1007/s11784-023-01095-3