Some Homotopy Groups of Homogeneous Spaces

Abstract

The symplectic group is embedded in the rotation group and the quotient set equipped with the identification topology is a homogeneous space. The purpose of this paper is to determine some homotopy groups of the homogeneous space. Exact sequences induced from fibrations are frequently used, and homotopy groups of Lie groups and other homogeneous spaces which are obtained by several authors are referred heavily.</p