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Spring Topology and Dynamical Systems Conference
March 15-17, 2001
Centro de Convenciones
Morelia City, Michoacán, Mexico

Organizers
Alejandro Illanes, Sergio Macías, Jesus Muciño, María Luisa Pérez

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1-bridge knots with respect to a torus and meridional surfaces
by
Mario Eudave-Muñoz
Instituto de Matemáticas, UNAM
Coauthors: Enrique Ramírez-Losada (Cimat)

We say that a knot k in S3 is of 1 bridge with respect to a torus, if there exists a standard torus T in S3, which intersects k in two points, dividing it into two arcs which project to simple arcs on T. If a knot is of 1 bridge w.r.t. a torus T, then it has tunnel number one.

Gordon and Reid proved that tunnel number one knots do not have any essential meridional planar surface. Here we show that the same is not true for surfaces of higher genus.

We prove that for each g >= 1, there are knots which are of 1 bridge w.r.t. a torus T, and which have an essential meridional surface of genus g.

Date received: February 9, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagh-67.