TY - JOUR

T1 - Automorphisms of pure braid groups

AU - Bardakov, Valeriy G.

AU - Neshchadim, Mikhail V.

AU - Singh, Mahender

N1 - Publisher Copyright: © 2017, Springer-Verlag GmbH Austria.

PY - 2018/9/1

Y1 - 2018/9/1

N2 - 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 .

AB - 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 .

KW - Braid group

KW - Central automorphism

KW - Extended mapping class group

KW - Pure braid group

KW - GROUP EXTENSIONS

UR - http://www.scopus.com/inward/record.url?scp=85020546801&partnerID=8YFLogxK

U2 - 10.1007/s00605-017-1073-7

DO - 10.1007/s00605-017-1073-7

M3 - Article

AN - SCOPUS:85020546801

VL - 187

SP - 1

EP - 19

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 1

ER -