Automorphisms of pure braid groups

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3 Citations (Scopus)


In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for n> 3 , Aut (P n ) is generated by the subgroup Aut c (P n ) of central automorphisms of P n , the subgroup Aut (B n ) of restrictions of automorphisms of B n on P n and one extra automorphism w n . We also investigate the lifting and extension problem for automorphisms of some well-known exact sequences arising from braid groups, and prove that that answers are negative in most cases. Specifically, we prove that no non-trivial central automorphism of P n can be extended to an automorphism of B n .

Original languageEnglish
Pages (from-to)1-19
Number of pages19
JournalMonatshefte fur Mathematik
Issue number1
Publication statusPublished - 1 Sep 2018


  • Braid group
  • Central automorphism
  • Extended mapping class group
  • Pure braid group


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