The classification and the conjugacy classes of the finite subgroups of the sphere braid groups


Autoria(s): GONCALVES, Daciberg L.; GUASCHI, John
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

20/10/2012

20/10/2012

2008

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

http://dx.doi.org/10.2140/agt.2008.8.757

Idioma(s)

eng

Publicador

GEOMETRY & TOPOLOGY PUBLICATIONS

Relação

Algebraic and Geometric Topology

Direitos

closedAccess

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Tipo

article

original article

publishedVersion