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Action of automorphisms of pure braid groups on homotopy groups of two-sphere

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arxiv 2112.05805 v2 pith:ESUVV7H7 submitted 2021-12-10 math.GR math.ATmath.GT

Action of automorphisms of pure braid groups on homotopy groups of two-sphere

classification math.GR math.ATmath.GT
keywords groupsbraidpureactionautomorphismshomotopytwo-sphereautomorphism
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We examine the Moore complex of the Delta-group structure related to the pure braid groups and introduced by Berrick, Cohen, Wong, and Wu. We prove that the cycle and the boundary groups are invariant under all automorphisms of the pure braid groups, and thereby, we extend the results of Li and Wu on the reflection automorphism. We conclude that there is an induced action of all automorphisms of the pure braid groups on the homotopy groups of the two-sphere. Besides, we compute this action for a small number of strands.

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