Automorphisms of pure braid groups | Sciact

Automorphisms of pure braid groups Full article

Journal

Monatshefte fur Mathematik
ISSN: 0026-9255 , E-ISSN: 1436-5081

Output data

Year: 2018, Volume: 187, Number: 1, Pages: 1-19 Pages count : 19 DOI: 10.1007/s00605-017-1073-7

Tags

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

Authors

Bardakov V.G. ^1,2,3,4 , Neshchadim M.V. ^1,2 , Singh M. ⁵

Affiliations

1	Sobolev Institute of Mathematics
2	Novosibirsk State University
3	Laboratory of Quantum Topology, Chelyabinsk State University, Brat’ev Kashirinykh Street 129, Chelyabinsk, 454001, Russian Federation
4	Novosibirsk State Agrarian University, Dobrolyubova Street, 160, Novosibirsk, 630039, Russian Federation
5	Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, P. O. Manauli, S. A. S. Nagar, Punjab, 140306, India

In this paper, we investigate the structure of the automorphism groups of pure braid groups. We prove that, for n> 3 , Aut (Pn) is generated by the subgroup Aut c(Pn) of central automorphisms of Pn, the subgroup Aut (Bn) of restrictions of automorphisms of Bn on Pn and one extra automorphism wn. 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 Pn can be extended to an automorphism of Bn. © 2017, Springer-Verlag GmbH Austria.

Bardakov V.G. , Neshchadim M.V. , Singh M.
Automorphisms of pure braid groups
Monatshefte fur Mathematik. 2018. V.187. N1. P.1-19. DOI: 10.1007/s00605-017-1073-7 WOS Scopus OpenAlex

Web of science:	WOS:000441529200001
Scopus:	2-s2.0-85020546801
OpenAlex:	W3103223877

DB	Citing
Scopus	4
OpenAlex	5
Web of science	3