On the locally finite chain algebra of a proper homotopy type

Abstract

In the classical paper [A-H] Adams-Hilton constructed a free chain algebra which is an important algebraic model of a simply connected homotopy type. We show that this chain algebra (endowed with an additional structure given by a “height function”) yields actually an invariant of a proper homotopy type. For this we introduce the homotopy category of locally finite chain algebras without using the usual methods of pro-categories. As examples we consider the locally finite chain algebras of Rn+1, S2×S2−{point}, and CP2−{point}.