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

  • Daciberg Lima Goncalves
  • John Guaschi

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Daciberg Lima Gonçalves, John Guaschi
    Pages 1-14
  3. Daciberg Lima Gonçalves, John Guaschi
    Pages 15-50
  4. Back Matter
    Pages 99-102

About this book


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. ​


20F36,20E07,20F50,55R80,55Q52 Configuration space Mapping class group Sphere braid groups Virtually cyclic group

Authors and affiliations

  • Daciberg Lima Goncalves
    • 1
  • John Guaschi
    • 2
  1. 1.Departamento de Matemática - IMEUniversidade de São PauloSão PauloBrazil
  2. 2.Laboratoire de Mathématiques Nicolas OresmeNormandie Université UNICAENCaen CedexFrance

Bibliographic information