Low Dimensional Actions of Semisimple Groups

摘要

For a simple non-compact Lie group G with finite center the author determines thesmallest integer n(G) such that G has an almost effective action on a compact manifold of dimension n(G), and characterize the compact manifolds of dimension n(G) on which G acts. The author studies actions of a semisimple group G on compact manifolds of dimension n(G) + 1 and determines the orbit structure of the action of G and its maximal compact subgroup. Several examples are given to illustrate the results.