# nLab Quillen plus construction

The Quillen plus construction is a method for simplifying the fundamental group of a space without changing its homology and cohomology groups. It was introduced by Kervaire (1969), but was crucially used Daniel Quillen to define higher algebraic K-theory? by applying it to the classifying space of the stable general linear group, $GL(A)$, of a ring $A$. It ‘kills’ a perfect normal subgroup of $G$ within the classifying space $BG$. For algebraic K-theory, that subgroup is the stable elementary linear group?, $E(A)$ within $GL(A)$

## References

• M. Kervaire,_Smooth homology spheres and their fundamental groups_, Trans. Amer. Math. Soc., 144 (1969) pp. 67–72
Created on February 3, 2012 14:39:44 by Tim Porter (95.147.237.181)