TY - BOOK ID - 8286127 TI - The classification of the virtually cyclic subgroups of the sphere braid groups AU - Lima Goncalves, Daciberg. AU - Guaschi, John. PY - 2013 SN - 3319002562 3319002570 PB - Cham : Springer International Publishing : Imprint: Springer, DB - UniCat KW - Braid theory. KW - Finite groups. KW - Group theory. KW - Braid theory KW - Group theory KW - Mathematics KW - Physical Sciences & Mathematics KW - Algebra KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Braids, Theory of KW - Theory of braids KW - Mathematics. KW - Algebra. KW - Algebraic topology. KW - Group Theory and Generalizations. KW - Algebraic Topology. KW - Knot theory KW - Low-dimensional topology KW - Mathematical analysis KW - Topology UR - https://www.unicat.be/uniCat?func=search&query=sysid:8286127 AB - 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. ER -