Homology of Linear Groups

1. Front Matter

   Pages i-xi

   PDF

2. Topological Methods

   • Kevin P. Knudson

   Pages 1-31

3. Stability

   • Kevin P. Knudson

   Pages 33-64

4. Low-dimensional Results

   • Kevin P. Knudson

   Pages 65-90

5. Rank One Groups

   • Kevin P. Knudson

   Pages 91-115

6. The Friedlander-Milnor Conjecture

   • Kevin P. Knudson

   Pages 117-147

7. Back Matter

   Pages 149-192

   PDF

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

"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

• Department of Mathematics, Wayne State University, Detroit, USA

  Kevin P. Knudson

Policies and ethics