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

Hiroshi Iriyeh; Takashi Sakai; Hiroyuki Tasaki

paper

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

arXiv:1108.0260

Abstract

In this paper we calculate the Lagrangian Floer homology $H F (L_{0}, L_{1} : Z_{2})$ of a pair of real forms $(L_{0}, L_{1})$ in a monotone Hermitian symmetric space $M$ of compact type in the case where $L_{0}$ is not necessarily congruent to $L_{1}$ . 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.

arXiv comment13 pages, to appear in Journal of the Mathematical Society of Japan