The Plus Construction
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 π1(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)).
KeywordsBase Point Spectral Sequence Homology Group Homotopy Type Connected Space
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