Algebraic K-Theory pp 21-34 | Cite as

# The Plus Construction

Chapter

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## Abstract

For any associative ring R, we regard GL(R) as a topological group with the discrete topology, and let BGL(R) denote the ‘classifying space’ of GL(R). For our purposes, it is only important to know that BGL(R) is an Eilenberg-MacLane space K(GL(R), 1) i.e. BGL(R) is a connected space with π_{1}(BGL(R))≅ GL(R), π_{i}(BGL(R)) = 0 for i≥2, and that these properties characterise BGL(R) upto homotopy equivalence (since we are assuming that all spaces considered here have the homotopy type of a CW-complex). We give a construction of the classifying space of a discrete group in the next chapter (Example (3.10)).

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## References

- J.-L. Loday: K-theorie algebrique et representation des groupes, Ann. Sci. Ecole form. Sup. 9(1976).Google Scholar
- G.W. Whitehead: Elements of homotopy theory, Grad. Texts in Math. fo.61, Springer-Verlag.Google Scholar
- These are cited below as [L] and [W] respectively.Google Scholar

## Copyright information

© Springer Science+Business Media New York 1991