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Homology of Linear Groups

  • Kevin P. Knudson

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

Introduction

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.

Keywords

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

Authors and affiliations

  • Kevin P. Knudson
    • 1
  1. 1.Department of MathematicsWayne State UniversityDetroitUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-8338-2
  • Copyright Information Birkhäuser Verlag 2001
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-0348-9523-1
  • Online ISBN 978-3-0348-8338-2
  • Series Print ISSN 0743-1643
  • Series Online ISSN 2296-505X
  • Buy this book on publisher's site