### A universal space for plus-constructions, by A. J. Berrick and Carles Casacuberta

To appear in Topology.
We exhibit a two-dimensional, acyclic, Eilenberg-MacLane space W such that,
for every space X, the plus-construction X^+ with respect to the largest
perfect subgroup of pi _1(X) coincides, up to homotopy, with the
W-nullification of X; that is, the natural map from X to X^+ is homotopy
initial among maps from X to Y where the based mapping space map(W,Y) is
weakly contractible. Furthermore, we describe the effect of W-nullification
for any acyclic W, and show that some of its properties imply, in their turn,
the acyclicity of W. This leads to a question concerning which spaces W have
the property that W-nullification coincides with the plus-construction on
spaces of type BGLR; such spaces may be said to define algebraic K-theory.

A. J. Berrick <berrick@math.nus.edu.sg>

Carles Casacuberta <casac@mat.uab.es>