© 2001

Homology of Linear Groups


Part of the Progress in Mathematics book series (PM, volume 193)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Kevin P. Knudson
    Pages 1-31
  3. Kevin P. Knudson
    Pages 33-64
  4. Kevin P. Knudson
    Pages 65-90
  5. Kevin P. Knudson
    Pages 91-115
  6. Kevin P. Knudson
    Pages 117-147
  7. Back Matter
    Pages 149-192

About this book


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.


Cohomology Homotopy K-theory algebra cohomology of groups homology homotopy theory

Authors and affiliations

  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

Bibliographic information

  • Book Title Homology of Linear Groups
  • Authors Kevin P. Knudson
  • Series Title Progress in Mathematics
  • Series Abbreviated Title Progress in Mathematics(Birkhäuser)
  • DOI
  • Copyright Information Birkhäuser Verlag 2001
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-7643-6415-1
  • Softcover ISBN 978-3-0348-9523-1
  • eBook ISBN 978-3-0348-8338-2
  • Series ISSN 0743-1643
  • Series E-ISSN 2296-505X
  • Edition Number 1
  • Number of Pages XI, 192
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebraic Topology
  • Buy this book on publisher's site


"A book for graduates and researchers in K-theory, cohomology, algebraic geometry and topology. The theme is the development of the computing of the homology of the groups of matrices from Daniel Quillen’s definitions of the higher algebraic K-groups. Stability theorems, low-dimensional results and the Friedlander-Milnor conjecture are discussed in this monograph."

–Aslib Book Guide

"This marks the first time that many of these results have been collected in a single volume…"

–Mathematical Reviews