Link Floer Homology and a Hofer Pseudometric on Braids
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913491622821888 |
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| author | Morabito, Francesco |
| author_facet | Morabito, Francesco |
| contents | Following an idea of Frédéric le Roux, we define in this paper a family of Hofer-type pseudonorms on braid groups, computing the minimal energy of a Hamiltonian diffeomorphism which fixes a Lagrangian configuration of circles on the unit disc and realises that braid type. We prove that in the case of braids with two strands we have in fact a norm, and we give lower estimates for braids with more strands. The main tool is Link Floer Homology, recently defined by D. Cristofaro-Gardiner, V. Humilière, C.-Y. Mak, S. Seyfaddini and I. Smith, which we use to construct a family of quasimorphisms on the group of compactly supported Hamiltonian diffeomorphisms which is sensitive to the linking number of diffeomorphisms fixing Lagrangian links. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08105 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Link Floer Homology and a Hofer Pseudometric on Braids Morabito, Francesco Symplectic Geometry 53D40, 37E30 Following an idea of Frédéric le Roux, we define in this paper a family of Hofer-type pseudonorms on braid groups, computing the minimal energy of a Hamiltonian diffeomorphism which fixes a Lagrangian configuration of circles on the unit disc and realises that braid type. We prove that in the case of braids with two strands we have in fact a norm, and we give lower estimates for braids with more strands. The main tool is Link Floer Homology, recently defined by D. Cristofaro-Gardiner, V. Humilière, C.-Y. Mak, S. Seyfaddini and I. Smith, which we use to construct a family of quasimorphisms on the group of compactly supported Hamiltonian diffeomorphisms which is sensitive to the linking number of diffeomorphisms fixing Lagrangian links. |
| title | Link Floer Homology and a Hofer Pseudometric on Braids |
| topic | Symplectic Geometry 53D40, 37E30 |
| url | https://arxiv.org/abs/2301.08105 |