Algebraic K-theory of Crystallographic Groups

The Three-Dimensional Splitting Case

  • Daniel Scott Farley
  • Ivonne Johanna Ortiz

Part of the Lecture Notes in Mathematics book series (LNM, volume 2113)

Table of contents

  1. Front Matter
    Pages i-x
  2. Daniel Scott Farley, Ivonne Johanna Ortiz
    Pages 1-8
  3. Daniel Scott Farley, Ivonne Johanna Ortiz
    Pages 9-21
  4. Daniel Scott Farley, Ivonne Johanna Ortiz
    Pages 23-39
  5. Daniel Scott Farley, Ivonne Johanna Ortiz
    Pages 41-43
  6. Daniel Scott Farley, Ivonne Johanna Ortiz
    Pages 45-57
  7. Daniel Scott Farley, Ivonne Johanna Ortiz
    Pages 59-79
  8. Daniel Scott Farley, Ivonne Johanna Ortiz
    Pages 99-117
  9. Daniel Scott Farley, Ivonne Johanna Ortiz
    Pages 119-136
  10. Daniel Scott Farley, Ivonne Johanna Ortiz
    Pages 137-141
  11. Back Matter
    Pages 143-150

About this book

Introduction

The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory. In cases where the conjecture is known to be a theorem, it gives a powerful method for computing the lower algebraic K-theory of a group. This book contains a computation of the lower algebraic K-theory of the split three-dimensional crystallographic groups, a geometrically important class of three-dimensional crystallographic group, representing a third of the total number. The book leads the reader through all aspects of the calculation. The first chapters describe the split crystallographic groups and their classifying spaces. Later chapters assemble the techniques that are needed to apply the isomorphism theorem. The result is a useful starting point for researchers who are interested in the computational side of the Farrell-Jones isomorphism conjecture, and a contribution to the growing literature in the field.

Keywords

20H15,19B28,19A31,19D35 Algebraic K-theory Classifying spaces Crystallographic groups Farrell-Jones isomorphism conjecture

Authors and affiliations

  • Daniel Scott Farley
    • 1
  • Ivonne Johanna Ortiz
    • 2
  1. 1.MathematicsMiami UniversityOxfordUSA
  2. 2.MathematicsMiami UniversityOxfordUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-08153-3
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-08152-6
  • Online ISBN 978-3-319-08153-3
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book