Overview
- Includes many worked examples of K-theory computations for finite groups
- A useful reference for researchers in K-theory, bringing together a broad array of techniques and references in one place, and mainly self-contained
- Applies the knowledge of virtually-cyclic subgroups to determine the lower algebraic K-theory for the braid groups of B4(S2)
- Gives new properties about braid groups of the sphere
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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Table of contents (4 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This volume deals with the K-theoretical aspects of the group rings of braid groups of the 2-sphere. The lower algebraic K-theory of the finite subgroups of these groups up to eleven strings is computed using a wide variety of tools. Many of the techniques extend to the general case, and the results reveal new K-theoretical phenomena with respect to the previous study of other families of groups. The second part of the manuscript focusses on the case of the 4-string braid group of the 2-sphere, which is shown to be hyperbolic in the sense of Gromov. This permits the computation of the infinite maximal virtually cyclic subgroups of this group and their conjugacy classes, and applying the fact that this group satisfies the Fibred Isomorphism Conjecture of Farrell and Jones, leads to an explicit calculation of its lower K-theory.
Researchers and graduate students working in K-theory and surface braid groups will constitute the primary audience of the manuscript, particularly those interested in the Fibred Isomorphism Conjecture, and the computation of Nil groups and the lower algebraic K-groups of group rings. The manuscript will also provide a useful resource to researchers who wish to learn the techniques needed to calculate lower algebraic K-groups, and the bibliography brings together a large number of references in this respect.Authors and Affiliations
Bibliographic Information
Book Title: The Lower Algebraic K-Theory of Virtually Cyclic Subgroups of the Braid Groups of the Sphere and of ZB4(S2)
Authors: John Guaschi, Daniel Juan-Pineda, Silvia Millán López
Series Title: SpringerBriefs in Mathematics
DOI: https://doi.org/10.1007/978-3-319-99489-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-99488-8Published: 13 November 2018
eBook ISBN: 978-3-319-99489-5Published: 03 November 2018
Series ISSN: 2191-8198
Series E-ISSN: 2191-8201
Edition Number: 1
Number of Pages: X, 80
Number of Illustrations: 4 b/w illustrations
Topics: Group Theory and Generalizations, K-Theory, Commutative Rings and Algebras