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

机译：紧型Hermitian对称空间中一对实形的Lagrangian Floer同源性

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In this paper we calculate the Lagrangian Floer homology HF(L_0,L_1 : Z2) 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.

机译：在本文中，我们计算紧凑型单调Hermitian对称空间M中一对实型（L_0，L_1）的拉格朗日Floer同源性HF（L_0，L_1：Z2），其中L_0不一定与L_1一致。特别地，在M不可约的情况下，我们对Arnold-Givental不等式进行了推广。作为其应用，我们证明了在二次哈密顿形变下，复杂二阶中的全测地拉格朗日球总体上具有最小的体积。

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来源
《Journal of the Mathematical Society of Japan》 |2013年第4期|1135-1151|共17页
作者
Hiroshi Iriyeh; Takashi Sakai; Hiroyuki Tasaki;
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作者单位

School of Science and Technology for Future Life Tokyo Denki University 5 Senju-Asahi-cho, Adachi-ku Tokyo 120-8551, Japan;

Department of Mathematics and Information Sciences Tokyo Metropolitan University Minami-osawa, Hachioji-shi Tokyo 192-0397, Japan;

Division of Mathematics Faculty of Pure and Applied Sciences University of Tsukuba Tsukuba, Ibaraki 305-8571, Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Lagrangian Floer homology; Hermitian symmetric space; real form; 2-number; Arnold-Givental inequality;

机译：拉格朗日Floer同源性;埃尔米特对称空间;真实形式2位数;Arnold-Givental不等式;

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6. Metric rigidity theorems on Hermitian locally symmetric spaces [O] . Ngaiming Mok 1986

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7. Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type [O] . IRIYEH Hiroshi, SAKAI Takashi, TASAKI Hiroyuki 2013

机译：紧型Hermitian对称空间中一对实形的Lagrangian Floer同源性

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

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