Real analytic actions of complex symplectic groups and other classical Lie groups on spheres (Q1819419)

The author studies analytic \(S_ p(n, {\mathbb{C}})\)-actions on integral homology k-spheres. Under certain technical hypotheses, the author characterizes such actions. The techniques and arguments are similar to the author's previous papers [Tôhoku Math. J., II. Ser. 33, 145-175 (1981; Zbl 0542.57032), and Bull. Yamagata Univ., Nat. Sci. 10, 1-14 (1980)]. A key theorem in the present paper is the author's theorem 2.1: Let SL(2, \({\mathbb{C}})\) act analytically on M such that the restricted SU(2)-action is almost free and each isotropy group contains a subgroup conjugate to L(1). Then the fixed point set of L(1) is an analytic submanifold of codimension two.