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2003•arXiv (Cornell University)Open access

Lagrangian spheres in S^2 x S^2

Richard Hind

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Abstract

We prove that all Lagrangian spheres in S^2 x S^2 are Hamiltonian isotopic. The proof uses various properties of holomorphic curves in symplectic manifolds with cylindrical ends which were recently developed in connection with the Symplectic Field Theory.

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We prove that all Lagrangian spheres in S^2 x S^2 are Hamiltonian isotopic. The proof uses various properties of holomorphic curves in symplectic manifolds with cylindrical ends which were recently developed in connection with the Symplectic Field Theory.

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Available abstract

We prove that all Lagrangian spheres in S^2 x S^2 are Hamiltonian isotopic. The proof uses various properties of holomorphic curves in symplectic manifolds with cylindrical ends which were recently developed in connection with the Symplectic Field Theory.

Key concepts: Symplectic geometry, SPHERES, Lagrangian, Holomorphic function, Hamiltonian (control theory), Symplectomorphism, Connection (principal bundle), Mathematics

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