WorkshopsLagrangian Floer homology and its application to Hamiltonian volume minimizing property
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The Lagrangian Floer homology $HF(L_0, L_1 : {\mathbb Z}_2)$ is an invariant of a pair of Lagrangian submanifolds $(L_0, L_1)$ in a symplectic manifold. In this talk we calculate $HF(L_0, L_1 : {\mathbb Z}_2)$ of a pair of real forms $(L_0, L_1)$ in a monotone Hermitian symmetric space of compact type in the case where $L_0$ is not necessarily congruent to $L_1$. This yields a generalization of the Arnold-Givental inequality. As an application, we obtain a volume estimate for real forms of the complex hyperquadric under Hamiltonian deformations. In particular, we prove that the totally geodesic Lagrangian sphere in the complex hyperquadric is Hamiltonian volume minimizing. This talk is based on a joint work with Hiroshi Iriyeh and Hiroyuki Tasaki.
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Takashi Sakai
2012-03-18
14:00:00 - 14:50:00
308 , Mathematics Research Center Building (ori. New Math. Bldg.)
The Lagrangian Floer homology $HF(L_0, L_1 : {\mathbb Z}_2)$ is an invariant of a pair of Lagrangian submanifolds $(L_0, L_1)$ in a symplectic manifold. In this talk we calculate $HF(L_0, L_1 : {\mathbb Z}_2)$ of a pair of real forms $(L_0, L_1)$ in a monotone Hermitian symmetric space of compact type in the case where $L_0$ is not necessarily congruent to $L_1$. This yields a generalization of the Arnold-Givental inequality. As an application, we obtain a volume estimate for real forms of the complex hyperquadric under Hamiltonian deformations. In particular, we prove that the totally geodesic Lagrangian sphere in the complex hyperquadric is Hamiltonian volume minimizing. This talk is based on a joint work with Hiroshi Iriyeh and Hiroyuki Tasaki.
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