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A Braided Simplicial Group
Author(s) -
Wu Jie
Publication year - 2002
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/s0024611502013370
Subject(s) - mathematics , braid group , group (periodic table) , braid , braid theory , homotopy , homotopy group , action (physics) , group action , pure mathematics , simplicial complex , combinatorics , algebra over a field , chemistry , materials science , physics , organic chemistry , quantum mechanics , composite material
By studying the braid group action on Milnor's construction of the 1‐sphere, we show that the general higher homotopy group of the 3‐sphere is the fixed set of the pure braid group action on certain combinatorially described groups. This establishes a relation between the braid groups and the homotopy groups of the sphere. 2000 Mathematical Subject Classification : 20F36, 55P35, 55Q05, 55Q40, 55U10.