Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type

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  • Iriyeh Hiroshi
    School of Science and Technology for Future Life, Tokyo Denki University
  • Sakai Takashi
    Department of Mathematics and Information Sciences, Tokyo Metropolitan University
  • Tasaki Hiroyuki
    Division of Mathematics, Faculty of Pure and Applied Sciences, University of Tsukuba

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  • Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type Japan

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In this paper we calculate the Lagrangian Floer homology HF(L0, L1 : ℤ2) of a pair of real forms (L0, L1) in a monotone Hermitian symmetric space M of compact type in the case where L0 is not necessarily congruent to L1. In particular, we have a generalization of the Arnold-Givental inequality in the case where M is irreducible. As its application, we prove that the totally geodesic Lagrangian sphere in the complex hyperquadric is globally volume minimizing under Hamiltonian deformations.

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