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The Stabilizer of 1 in Habegger-Lin's Action for String Links

Pires de CAMPOS, José Eduardo Prado

Tokyo journal of mathematics, 2010-12, Vol.33 (2), p.311-326 [Periódico revisado por pares]

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Título:
The Stabilizer of 1 in Habegger-Lin's Action for String Links
Autor: Pires de CAMPOS, José Eduardo Prado
Assuntos: 57M25
É parte de: Tokyo journal of mathematics, 2010-12, Vol.33 (2), p.311-326
Descrição: Let H(k) be the group of all homotopy classes of k-string links. It has been proved that f,g\in H(k) have the same closure if and only if there is \beta\in S_k(1) such that \beta\cdot f=g, where S_k(1) is the stabilizer of 1 for a certain action of the group H(2k) on the set H(k). If \beta\in S_k(1), Artin's automorphism \overline{\beta}, induced by \beta on RF(2k), the reduced free group in 2k generators, induces an automorphism \overline{\overline{\beta}}\in A(RF(k)), the group of all automorphisms of RF(k) that send each generator to one of its conjugates. This can be used to compare the homotopy classes of links obtained by closing f and g. The association \beta\mapsto \overline{\overline{\beta}} is a homomorphism from S_k(1) to A(RF(k)). In this paper we determine its kernel.
Editor: Publication Committee for the Tokyo Journal of Mathematics
Idioma: Inglês

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