2000/10/12 by M. Arkowitz, G. Lupton
Mathematics · #math.AT #msc:55P62 #msc:55Q05 #msc:55S35 #msc:55P10
published as Math. Zeit., Vol. 235 (2000), 525--539. · To appear, Math. Zeit
arxiv created 2000/10/12 · arxiv updated 2009/11/30
We develop an obstruction theory for homotopy of homomorphisms f,g : M -> N between minimal differential graded algebras. We assume that M = Lambda V has an obstruction decomposition given by V = V0 oplus V1 and that f and g are homotopic on Lambda V0. An obstruction is then obtained as a vector space homomorphism V1 -> H^*(N). We investigate the relationship between the condition that f and g are homotopic and the condition that the obstruction is zero. The obstruction theory is then applied to study the set of homotopy classes [M, N]. This enables us to give a fairly complete answer to a conjecture of Copeland-Shar on the size of the homotopy set [A,B] when A and B are rational spaces. In addition, we give examples of minimal algebras (and hence of rational spaces) that have few homotopy classes of self-maps.