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The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups

English · Paperback / Softback

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Description

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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.

List of contents

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.

Summary

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.

Product details

Authors John Guaschi, Daciber Lima Goncalves, Daciberg Lima Goncalves
Publisher Springer, Berlin
 
Languages English
Product format Paperback / Softback
Released 02.03.2013
 
EAN 9783319002569
ISBN 978-3-31-900256-9
No. of pages 102
Dimensions 155 mm x 235 mm x 6 mm
Weight 184 g
Illustrations X, 102 p. 26 illus.
Series SpringerBriefs in Mathematics
SpringerBriefs in Mathematics
Subject Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra

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