Twisting cochains and duality between minimal algebras and minimal Lie algebras

Abstract

An algebraic duality theory is developed between 1 1 -connected minimal cochain algebras of finite type and connected minimal chain Lie algebras of finite type by means of twisting cochains. The duality theory gives a concrete relationship between Sullivan’s minimal models, Chen’s power series connections and the various Lie algebra models of a 1 1 -connected topological space defined by Quillen, Allday, Baues-Lemaire and Neisendorfer. It can be used to compute the Lie algebra model of a space from the algebra model of the space and vice versa.