Rational Pontrjagin Homology Ring of the Based Loop Space on Some Homogeneous Spaces

Abstract

In this paper we consider the rational homology of the based loop space on the class of compact, connected homogeneous spaces, known as the generalised symmetric spaces. Due to the results from [11] and [12] together with Milnor-Moore theorem, it is possible to explicitly describe the rational Pontrjagin homology ring of the based loop space on these spaces. By making use of that, we prove some general results on their based loop space rational homology ring and provide an explicit description of the rational Pontrjagin homology ring for some irreducible, simply connected symmetric spaces.