Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Towards a characterization of smooth braids

D. L. Johnsona1

a1 University of Nottingham

The braid group on n + 1 strings has the presentation

S0305004100060138_eqn1

where xi corresponds to the single crossing of the i string over the i + 1 string, and rij is a commutator S0305004100060138_inline1 when i < j − 1, and a braid relator S0305004100060138_inline2 when i = j − 1. B1 is the trivial group and B2 is infinite cyclic; we shall assume n ≥ 2 throughout.

(Received March 31 1982)