ENGLISH

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

By Daciberg Lima Goncalves , John Guaschi (auth.)

Book information

Publisher
Springer International Publishing
Year
2013
ISBN
978-3-319-00256-9, 978-3-319-00257-6
DOI
10.1007/978-3-319-00257-6
Language
english
Format
PDF
Filesize
2 MB (1585499 bytes)
Series
SpringerBriefs in Mathematics
Edition
1
Pages
102\111
Orientation
yes
Scanned
yes
Time added
2013-09-13 13:34:25
Group Theory and Generalizations; Algebraic Topolo

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. ​

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