Algebraic K-Theory pp 18-30 | Cite as

# The Plus Construction

Chapter

## 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 characterize *BGL*(*R*) up to 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)).

## Keywords

Base Point Spectral Sequence Homology Group Homotopy Type Connected Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1996