Commutative rings, algebraic topology, graded Lie algebras and the work of Jan-Erik Roos (Q1063679)

For a 1-connected CW complex of finite type X topologists have been interested in the graded algebra \(H_*(\Omega X;{\mathbb{Q}})\), \(\Omega\) X being the loop space of X. Algebraists have studied the graded algebra \(Ext^*_ R(k,k)\), (R,m,k) being a local ring. It has been realized that the two fields - rational homotopy theory and local rings - share a common body of techniques but also of theorems. This article is written in honour to Jan-Erik Roos who was the first to realize the strong connection between the two fields. The article overviews results achieved in this area (on both sides) for the last decades.