The classification and the conjugacy classes of the finite subgroups of the sphere braid groups
Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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Data(s) |
20/10/2012
20/10/2012
2008
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Resumo |
Let n >= 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*; the binary octahedral group O*; 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)). |
Identificador |
ALGEBRAIC AND GEOMETRIC TOPOLOGY, v.8, n.2, p.757-785, 2008 1472-2739 http://producao.usp.br/handle/BDPI/30658 10.2140/agt.2008.8.757 |
Idioma(s) |
eng |
Publicador |
GEOMETRY & TOPOLOGY PUBLICATIONS |
Relação |
Algebraic and Geometric Topology |
Direitos |
closedAccess Copyright GEOMETRY & TOPOLOGY PUBLICATIONS |
Palavras-Chave | #MAPPING CLASS-GROUPS #Z/A X Z/B #SELF-EQUIVALENCES #HOMOTOPY TYPES #SPACE-FORMS #CONFIGURATION-SPACES #RIEMANN SURFACE #Mathematics |
Tipo |
article original article publishedVersion |