Quantitative Heegaard Floer cohomology and the Calabi invariant
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866913290896015360 |
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| author | Cristofaro-Gardiner, Daniel Humilière, Vincent Mak, Cheuk Yu Seyfaddini, Sobhan Smith, Ivan |
| author_facet | Cristofaro-Gardiner, Daniel Humilière, Vincent Mak, Cheuk Yu Seyfaddini, Sobhan Smith, Ivan |
| contents | We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications, we resolve several open questions from topological surface dynamics and continuous symplectic topology: we show that the group of Hamiltonian homeomorphisms of any compact surface with (possibly empty) boundary is not simple; we extend the Calabi homomorphism to the group of Hameomorphisms constructed by Oh-Müller; and, we construct an infinite dimensional family of quasimorphisms on the group of area and orientation preserving homeomorphisms of the two-sphere. Our invariants are inspired by recent work of Polterovich and Shelukhin defining and applying spectral invariants for certain classes of links in the two-sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_11026 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Quantitative Heegaard Floer cohomology and the Calabi invariant Cristofaro-Gardiner, Daniel Humilière, Vincent Mak, Cheuk Yu Seyfaddini, Sobhan Smith, Ivan Symplectic Geometry Dynamical Systems Geometric Topology 53D40 37E30 We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi invariant of Hamiltonians in their limit. As applications, we resolve several open questions from topological surface dynamics and continuous symplectic topology: we show that the group of Hamiltonian homeomorphisms of any compact surface with (possibly empty) boundary is not simple; we extend the Calabi homomorphism to the group of Hameomorphisms constructed by Oh-Müller; and, we construct an infinite dimensional family of quasimorphisms on the group of area and orientation preserving homeomorphisms of the two-sphere. Our invariants are inspired by recent work of Polterovich and Shelukhin defining and applying spectral invariants for certain classes of links in the two-sphere. |
| title | Quantitative Heegaard Floer cohomology and the Calabi invariant |
| topic | Symplectic Geometry Dynamical Systems Geometric Topology 53D40 37E30 |
| url | https://arxiv.org/abs/2105.11026 |