Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces of compact type
| Autor: | Takashi Sakai, Hiroshi Iriyeh, Hiroyuki Tasaki |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Hermitian symmetric space Primary 53D40 Secondary 53D12 Generalization General Mathematics 53D40 Real form Type (model theory) symbols.namesake FOS: Mathematics Lagrangian Floer homology Mathematics::Symplectic Geometry Mathematics Mathematics::Functional Analysis real form Hermitian matrix 53D12 2-number Monotone polygon Arnold-Givental inequality Floer homology Differential Geometry (math.DG) Mathematics - Symplectic Geometry symbols Symplectic Geometry (math.SG) Hamiltonian (quantum mechanics) |
| Zdroj: | J. Math. Soc. Japan 65, no. 4 (2013), 1135-1151 |
| ISSN: | 0025-5645 |
| Popis: | 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. Comment: 13 pages, to appear in Journal of the Mathematical Society of Japan |
| Databáze: | OpenAIRE |
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