Premium
Artin braid groups and homotopy groups
Author(s) -
Li Jingyan,
Wu Jie
Publication year - 2009
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdp005
Subject(s) - mathematics , braid group , modulo , homotopy group , braid , braid theory , quotient , pure mathematics , homotopy , boundary (topology) , quotient group , combinatorics , mathematical analysis , cyclic group , abelian group , materials science , composite material
We study the Brunnian subgroups and the boundary Brunnian subgroups of the Artin braid groups. The general higher homotopy groups of the sphere are given by mirror symmetric elements in the quotient groups of the Artin braid groups modulo the boundary Brunnian braids, as well as given as summands of the centres of the quotient groups of Artin pure braid groups modulo boundary Brunnian braids. The results give new connections between the braid groups and the general higher homotopy groups of spheres.