Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Incompressible surfaces in the exterior of a closed 3-braid

I. Surfaces with horizontal boundary components

María Teresa Lozanoa1 and Józef H. Przytyckia2

a1 Facultad de Ciencias, Universidad de Zaragoza, Spain

a2 Department of Mathematics, University of Warsaw, Poland

Let S0305004100063465_inline1 be a closed 3-braid in S3 with axis Lγ. The exterior of γS0305004100063465_inline1 U Lγ in S3 is a fibre bundle over S1 with fibre a disc with 3 holes. The monodromy is given by a matrix in PSL(2,S0305004100063465_xs1D56B) and the braid γS0305004100063465_inline1 is called hyperbolic if its matrix is hyperbolic.

(Received June 11 1984)

(Revised January 17 1985)