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$ K\sb{3}$ of a ring is $ H\sb{3}$ of the Steinberg group

Author: S. M. Gersten
Journal: Proc. Amer. Math. Soc. 37 (1973), 366-368
MSC: Primary 18F25
MathSciNet review: 0320114
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Abstract: A proof of the result of the title is given using standard results of algebraic topology.

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  • [2] Michel A. Kervaire, Multiplicateurs de Schur et 𝐾-théorie, Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, New York, 1970, pp. pp 212–225 (French). MR 0274558
  • [3] S. Mac Lane, Homology, Die Grundlehren der math. Wissenschaften, Band 114, Academic Press, New York; Springer-Verlag, Berlin, 1963. MR 28 #122.
  • [4] Daniel Quillen, Cohomology of groups, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 47–51. MR 0488054
  • [5] -, Cohomology of groups and algebraic K-theory, Amer. Math. Soc. Winter Meeting, Atlantic City, N.J., 1971.
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Keywords: $ {K_3}$ of a ring, Steinberg group, third homology group of a group, central extension
Article copyright: © Copyright 1973 American Mathematical Society