SpringerBriefs in Mathematics

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

Authors: Lima Goncalves, Daciberg, Guaschi, John

Free Preview

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-319-00257-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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. ​

Table of contents (3 chapters)

Table of contents (3 chapters)
  • Introduction and Statement of the Main Results

    Pages 1-14

    Lima Gonçalves, Daciberg (et al.)

  • Virtually Cyclic Groups: Generalities, Reduction and the Mapping Class Group

    Pages 15-50

    Lima Gonçalves, Daciberg (et al.)

  • Realisation of the Elements of $$\mathbb V _{1}(n)$$ and $$\mathbb V _{2}(n)$$ in $$B_{n}(\mathbb{S }^{2})$$

    Pages 51-98

    Lima Gonçalves, Daciberg (et al.)

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-319-00257-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2013
Publisher
Springer International Publishing
Copyright Holder
John Guaschi
eBook ISBN
978-3-319-00257-6
DOI
10.1007/978-3-319-00257-6
Softcover ISBN
978-3-319-00256-9
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 102
Number of Illustrations
26 b/w illustrations
Topics