We give a description of all (1,2)–knots in S3
which admit a closed meridionally incompressible surface of genus 2 in their complement.
That is, we give several constructions of (1,2)–knots having a meridionally incompressible
surface of genus 2, and then show that any such surface for a
(1,2)–knot must come
from one of the constructions. As an application, we show explicit examples of tunnel number
one knots which are not (1,2)–knots.
Keywords
(1,2)–knot, meridionally
incompressible surface, tunnel number one knot
Instituto de Matemáticas
Universidad Nacional Autónoma de México
Ciudad Universitaria
04510 México D.F.
MEXICO
and
Centro de Investigación en Matemáticas
Apdo. Postal 402
36000 Guanajuato, Gto.
MEXICO