On symmetric commutator subgroups, braids, links and homotopy groups

J. Wu; J. Y. Li

arxiv: 1002.0429 · v1 · pith:HO3W3OHC · submitted 2010-02-02 · math.AT · math.GR· math.GT

On symmetric commutator subgroups, braids, links and homotopy groups

J. Y. Li , J. Wu This is my paper

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keywords groupssubgroupshomotopycommutatorlinkssomesymmetricapplications

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In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This gives a connection between links and homotopy groups. Similar results hold for braid and surface groups.

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On symmetric commutator subgroups, braids, links and homotopy groups

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