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The classification and the conjugacy classes of the finite subgroups of the sphere braid groups
- Source :
- Algebraic and Geometric Topology 8, 2 (2008) 757?785
- Publication Year :
- 2007
-
Abstract
- 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).<br />Comment: 23 pages
Details
- Database :
- arXiv
- Journal :
- Algebraic and Geometric Topology 8, 2 (2008) 757?785
- Publication Type :
- Report
- Accession number :
- edsarx.0711.3968
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.2140/agt.2008.8.757