The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups, 1st Edition

  • Published By:
  • ISBN-10: 3319002570
  • ISBN-13: 9783319002576
  • DDC: 514.224
  • Grade Level Range: College Freshman - College Senior
  • 102 Pages | eBook
  • Original Copyright 2013 | Published/Released May 2014
  • This publication's content originally published in print form: 2013

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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. ‚Äč

Table of Contents

Front Cover.
Other Frontmatter.
Title Page.
Copyright Page.
1: Introduction and Statement of the Main Results.
2: Virtually Cyclic Groups: Generalities, Reduction and the Mapping Class Group.
3: Realisation of the Elements of V1(n) and V2(n) in Bn(S2).
The Subgroups of the Binary Polyhedral Groups.