Text only print
Full screen print
Geometry Colloquium
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|
2014/06/19
10:00-11:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Takashi Sakai (Tokyo Metropolitan University)
Antipodal structure of the intersection of real forms and its applications (JAPANESE)
Takashi Sakai (Tokyo Metropolitan University)
Antipodal structure of the intersection of real forms and its applications (JAPANESE)
[ Abstract ]
A subset A of a Riemannian symmetric space is called an antipodal set if the geodesic symmetry s_x fixes all points of A for each x in A. This notion was first introduced by Chen and Nagano. Tanaka and Tasaki proved that the intersection of two real forms L_1 and L_2 in a Hermitian symmetric space of compact type is an antipodal set of L_1 and L_2. As an application, we calculate the Lagrangian Floer homology of a pair of real forms in a monotone Hermitian symmetric space. Then we obtain a generalization of the Arnold-Givental inequality. We expect to generalize the above results to the case of complex flag manifolds. In fact, using the k-symmetric structure, we can describe an antipodal set of a complex flag manifold. Moreover we can observe the antipodal structure of the intersection of certain real forms in a complex flag manifold.
This talk is based on a joint work with Hiroshi Iriyeh and Hiroyuki Tasaki.
A subset A of a Riemannian symmetric space is called an antipodal set if the geodesic symmetry s_x fixes all points of A for each x in A. This notion was first introduced by Chen and Nagano. Tanaka and Tasaki proved that the intersection of two real forms L_1 and L_2 in a Hermitian symmetric space of compact type is an antipodal set of L_1 and L_2. As an application, we calculate the Lagrangian Floer homology of a pair of real forms in a monotone Hermitian symmetric space. Then we obtain a generalization of the Arnold-Givental inequality. We expect to generalize the above results to the case of complex flag manifolds. In fact, using the k-symmetric structure, we can describe an antipodal set of a complex flag manifold. Moreover we can observe the antipodal structure of the intersection of certain real forms in a complex flag manifold.
This talk is based on a joint work with Hiroshi Iriyeh and Hiroyuki Tasaki.
