Geometry Colloquium

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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)
[ 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.