The Plus Construction

  • V. Srinivas
Part of the Progress in Mathematics book series (PM, volume 90)


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), πi(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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  1. J.-L. Loday: K-theorie algebrique et representation des groupes, Ann. Sci. Ecole form. Sup. 9(1976).Google Scholar
  2. G.W. Whitehead: Elements of homotopy theory, Grad. Texts in Math. fo.61, Springer-Verlag.Google Scholar
  3. These are cited below as [L] and [W] respectively.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • V. Srinivas
    • 1
  1. 1.School of MathematicsTata Institute of Fundamental ResearchBombayIndia

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