Ebook: Homology of Linear Groups

Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices. This text traces the development of this theory from Quillen's fundamental calculation of the cohomology of GLn (Fq). The stability theorems and low-dimensional results of A. Suslin, W. van der Kallen and others are presented as well as recent results for rank one groups. A chapter on the Friedlander-Milnor-conjecture concerning the homology of algebraic groups made discrete is also included. This marks the first time that these results have been collected in a single volume. The book should prove useful to graduate students and researchers in K-theory, group cohomology, algebraic geometry and topology.

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A text tracing the development of Daniel Quillen's theory of the higher algebraic K-groups which emphasizes the importance of computing homology of groups of matrices. Collects the results of a thorough examination of this and the related theorems. Of interest to researchers in K-theory, group homology, algebraic geometry, and topology.