The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups
1st Edition
Published on 8. September 2013
X, 102 pages
978-3-319-00257-6 (ISBN)
Description
This manuscript is devoted to classifying the isomorphism classes of the virtually cyclic subgroups of the braid groups of the 2-sphere. As well as enabling us to understand better the global structure of these groups, it marks an important step in the computation of the K-theory of their group rings. The classification itself is somewhat intricate, due to the rich structure of the finite subgroups of these braid groups, and is achieved by an in-depth analysis of their group-theoretical and topological properties, such as their centralisers, normalisers and cohomological periodicity. Another important aspect of our work is the close relationship of the braid groups with mapping class groups. This manuscript will serve as a reference for the study of braid groups of low-genus surfaces, and isaddressed to graduate students and researchers in low-dimensional, geometric and algebraic topology and in algebra.
More details
Series
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Product notice
Reflowable
Illustrations
X, 102 p. 26 illus.
File size
1,88 MB
ISBN-13
978-3-319-00257-6 (9783319002576)
DOI
10.1007/978-3-319-00257-6
Schweitzer Classification
Other editions
Additional editions
Daciberg Lima Goncalves | John Guaschi
The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups
Book
09/2013
1st Edition
Springer
€53.49
Shipment within 10-15 days
Content
Introduction and statement of the main results.- Virtually cyclic groups: generalities, reduction and the mapping class group.- Realisation of the elements of V1(n) and V2(n) in Bn(S2).- Appendix: The subgroups of the binary polyhedral groups.- References.
