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

John Guaschi

ISBN 10: 3319002562 / ISBN 13: 9783319002569

Published by Springer International Publishing Sep 2013, 2013

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 112 pp. Englisch.

Seller Inventory # 9783319002569

Bibliographic Details

• Title: The Classification of the Virtually Cyclic Subgroups of the Sphere Braid Groups
• Publisher: Springer International Publishing Sep 2013
• Publication Date: 2013
• Language: English
• ISBN 10: 3319002562
• ISBN 13: 9783319002569
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 7D millimeters 235 millimeters width by 155 millimeters height by 7 millimeters depth
• Weight: 184 grams

About this title

Synopsis

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. ​