Commutative rings, algebraic topology, graded Lie algebras and the work of Jan-Erik Roos
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.
scientific article; zbMATH DE number 3916532
scientific article