Automorphisms of pure braid groups

作者：Bardakov Valeriy G; Neshchadim Mikhail V; Singh Mahender^*

来源：Monatshefte fur Mathematik, 2018, 187(1): 1-19.

DOI：10.1007/s00605-017-1073-7

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

In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for , is generated by the subgroup of central automorphisms of , the subgroup of restrictions of automorphisms of on and one extra automorphism . 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 can be extended to an automorphism of B-n.

• 出版日期2018-9