Disk potential functions for quadrics

Kim, Yoosik

doi:10.1007/s11784-023-01049-9

J. Fixed Point Theory Appl.

2023

DOI: 10.1007/s11784-023-01049-9

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Disk potential functions for quadrics

Yoosik Kim

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Cited by 2 publications

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Hofer geometry via toric degeneration

Kawamoto

2023

Math. Ann.

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The main theme of this paper is to use toric degeneration to study Hofer geometry by producing distinct homogeneous quasimorphisms on the group of Hamiltonian diffeomorphisms. We focus on the (complex n-dimensional) quadric hypersurface and the del Pezzo surfaces, and study two classes of distinguished Lagrangian submanifolds that appear naturally in a toric degeneration, namely the Lagrangian torus which is the monotone fiber of a Lagrangian torus fibration, and the Lagrangian spheres that appear as vanishing cycles. For the quadrics, we prove that the group of Hamiltonian diffeomorphisms admits two distinct homogeneous quasimorphisms and derive some superheaviness results. Along the way, we show that the toric degeneration is compatible with the Biran decomposition. This implies that for $$n=2$$ n = 2 , the Lagrangian fiber torus (Gelfand–Zeitlin torus) is Hamiltonian isotopic to the Chekanov torus, which answers a question of Y. Kim. We prove analogous results for the del Pezzo surfaces. We also discuss applications to $$C^0$$ C 0 symplectic topology.

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Hofer geometry via toric degeneration

Kawamoto

2023

Math. Ann.

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Chekanov torus and Gelfand–Zeitlin torus in S2 × S2

Kim

2024

Differential Geometry and its Applications

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Disk potential functions for quadrics

Cited by 2 publications

References 39 publications

Hofer geometry via toric degeneration

Hofer geometry via toric degeneration

Chekanov torus and Gelfand–Zeitlin torus in S2 × S2

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Disk potential functions for quadrics

Cited by 2 publications

References 39 publications

Hofer geometry via toric degeneration

Hofer geometry via toric degeneration

Chekanov torus and Gelfand–Zeitlin torus in S2 × S2

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Chekanov torus and Gelfand–Zeitlin torus in S2 × S2