The classification and the conjugacy classes of the finite subgroups of the sphere braid groups
| dc.creator | Gonçalves, Daciberg Lima | |
| dc.creator | Guaschi, John | |
| dc.date | 2007-11-26 | |
| dc.date.accessioned | 2026-07-07T13:07:27Z | |
| dc.date.available | 2026-07-07T13:07:27Z | |
| dc.description | Let n\geq 3. We classify the finite groups which are realised as subgroups of the sphere braid group B_n(S^2). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B_n(S^2): Z_{2(n-1)}; the dicyclic groups of order 4n and 4(n-2); the binary tetrahedral group T_1; the binary octahedral group O_1; and the binary icosahedral group I. We give geometric as well as some explicit algebraic constructions of these groups in B_n(S^2), and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi's classification of the torsion elements of B_n(S^2), and explain how the finite subgroups of B_n(S^2) are related to this classification, as well as to the lower central and derived series of B_n(S^2). | |
| dc.description | 23 pages | |
| dc.identifier | https://arxiv.org/abs/0711.3968 | |
| dc.identifier | http://arxiv.org/abs/0711.3968 | |
| dc.identifier | Algebraic and Geometric Topology 8, 2 (2008) 757?785 | |
| dc.identifier | doi:10.2140/agt.2008.8.757 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/228093 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 20F36, 20F50, 20E45, 57M99 | |
| dc.title | The classification and the conjugacy classes of the finite subgroups of the sphere braid groups | |
| dc.type | text |