The involutions of the compact symmetric spaces (Q1109350)

The main purpose of this paper is to determine the fixed point sets of the involutions of the compact symmetric spaces. (Here, an involution is any involutive diffeomorphism which commutes with the symmetries of the given space.) The main geometric tool is attaching to any compact symmetric space a couple (M \(+,M\)-) of symmetric subspaces, which was introduced by \textit{B. Y. Chen} and the present author [see Duke Math. J. 44, 745-755 (1977; Zbl 0368.53038) and 45, 405-425 (1978; Zbl 0384.53024)]. Here M \(+\) means a connected component of the fixed point set with respect to a usual symmetry and M - is its ``orthogonal complement'' in a good sense. The author presents interesting relations to various topological and geometrical concepts and problems, such as the determination of the signature \(\tau\) (M), the Bott periodicity, the Chow arithmetic distance, and the Radon duality.