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arXiv · 1108.0260

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

Hiroshi Iriyeh·Takashi Sakai·Hiroyuki Tasaki
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Abstract

In this paper we calculate the Lagrangian Floer homology $HF(L_0, L_1 : {\mathbb Z}_2)$ 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.

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Hiroshi Iriyeh, Takashi Sakai, Hiroyuki Tasaki. 2012-07-01. Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type. https://arxiv.org/abs/1108.0260

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