Lecture Notes in Mathematics

Algebraic K-theory of Crystallographic Groups

The Three-Dimensional Splitting Case

Authors: Farley, Daniel Scott, Ortiz, Ivonne Johanna

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  • Contains an elementary classification of the arithmetic classes of three-dimensional crystallographic groups
  • Gives a clear construction, for a geometrically important class of groups, of the classifying spaces that are used in applications of the Farrell-Jones isomorphism conjecture
  • Shows how the Farrell-Jones isomorphism theorem is used in computations, assembling all of the required methods
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  • ISBN 978-3-319-08153-3
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About this book

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.

Table of contents (10 chapters)

Table of contents (10 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-319-08153-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-319-08152-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic K-theory of Crystallographic Groups
Book Subtitle
The Three-Dimensional Splitting Case
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2113
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-08153-3
DOI
10.1007/978-3-319-08153-3
Softcover ISBN
978-3-319-08152-6
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 148
Topics