GENERALIZED PLUS-CONSTRUCTIONS AND FUNDAMENTAL-GROUPS

Any generalized homology theory induces a generalized plus constructio n. We describe the effect of these plus-constructions upon fundamental groups. As a special case, we show that the generalized plus-construc tion associated to complex K-theory induces the same map on fundamenta l groups as Quillen's plus-construction with respect to the perfect ra dical. To do this, we identify Quillen's plus-construction with the Bo usfield nullification of a space with respect to the wedge of all coun table H(-;Z)-acyclic spaces. (C) 1998 Elsevier Science B.V. All right s reserved.