Haken manifolds obtained by surgery on closed pure 3-braids
by
Lorena Armas-Sanabria
Instituto de Matemáticas, UNAM

We consider 3-manifolds obtained by Dehn surgery on closed pure 3-braids, and are interested in studying the property P for that class of links.

Let L' = {[^(\beta)] subset S³: \beta = \prod₁ⁿ \sigma₁^2e_i \sigma₂^2f_i } be such that |e_i| > 1, |f_i| > 1. It is proved that under certain conditions on the surgery coefficients of elements of L', the manifolds obtained are Haken.

Date received: February 9, 2001