Algebraic K-theory of Crystallographic Groups: The Three-Dimensional Splitting Case

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Daniel Scott Farley Ivonne Johanna Ortiz

Algebraic K-theory of Crystallographic Groups

The Three-Dimensional Splitting Case

Daniel Scott Farley, Ivonne Johanna Ortiz

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English

Springer International Publishing AG
09 September 2014

Groups & group theory; Analytic geometry; Algebraic topology

Series: Lecture Notes in Mathematics

Summary
Details

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.

By: Daniel Scott Farley, Ivonne Johanna Ortiz
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2014 ed.
Volume: 2113
Dimensions: Height: 235mm, Width: 155mm, Spine: 9mm
Weight: 2.526kg
ISBN: 9783319081526
ISBN 10: 3319081527
Series: Lecture Notes in Mathematics
Pages: 148
Publication Date: 09 September 2014
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active