On link quasimorphisms on the sphere and the equator conjecture
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916956336029696 |
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| author | Serraille, Baptiste Trifa, Ibrahim |
| author_facet | Serraille, Baptiste Trifa, Ibrahim |
| contents | Link spectral invariants were introduced by Cristofaro-Gardiner, Humilière, Mak, Seyfaddini, and Smith. They induce Hofer-Lipschitz quasimorphisms on the group of Hamiltonian diffeomorphisms of the two-dimensional sphere. We prove that some linear combinations of those quasimorphisms vanish on the stabiliser of the equator. As a consequence, at least one of the following statements holds: there are non-trivial linear relations between the link quasimorphisms, or the space of equators of the sphere has infinite Hofer diameter. The proof relies on an `almost' Künneth formula in Link Floer Homology for some specific type of connected sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14996 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On link quasimorphisms on the sphere and the equator conjecture Serraille, Baptiste Trifa, Ibrahim Symplectic Geometry Link spectral invariants were introduced by Cristofaro-Gardiner, Humilière, Mak, Seyfaddini, and Smith. They induce Hofer-Lipschitz quasimorphisms on the group of Hamiltonian diffeomorphisms of the two-dimensional sphere. We prove that some linear combinations of those quasimorphisms vanish on the stabiliser of the equator. As a consequence, at least one of the following statements holds: there are non-trivial linear relations between the link quasimorphisms, or the space of equators of the sphere has infinite Hofer diameter. The proof relies on an `almost' Künneth formula in Link Floer Homology for some specific type of connected sums. |
| title | On link quasimorphisms on the sphere and the equator conjecture |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2509.14996 |