Journal of the Mathematical Society of Japan

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

Hiroshi IRIYEH, Takashi SAKAI, and 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.

Article information

Source
J. Math. Soc. Japan, Volume 65, Number 4 (2013), 1135-1151.

Dates
First available in Project Euclid: 24 October 2013

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1382620189

Digital Object Identifier
doi:10.2969/jmsj/06541135

Mathematical Reviews number (MathSciNet)
MR3127820

Zentralblatt MATH identifier
1281.53083

Subjects
Primary: 53D40: Floer homology and cohomology, symplectic aspects
Secondary: 53D12: Lagrangian submanifolds; Maslov index

Keywords
Lagrangian Floer homology Hermitian symmetric space real form 2-number Arnold-Givental inequality

Citation

IRIYEH, Hiroshi; SAKAI, Takashi; TASAKI, Hiroyuki. Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type. J. Math. Soc. Japan 65 (2013), no. 4, 1135--1151. doi:10.2969/jmsj/06541135. https://projecteuclid.org/euclid.jmsj/1382620189


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