A Seifert Algorithm for Knotted Surfaces
A bunch of cross sections of a
knotted surface are illustrated below.
With time I will draw these in more
detail and color. Read Further.
In the paper " A Seifert Algorithm for Knotted
by Carter and Saito a Seifert solid is constructed algorithmically
for any oriented knotted surface in 4-space.
One such example is given in Fox's famous
paper " A Quick Trip Through Knot Theory ".
Here we depict this knotted surface
as a broken surface diagram, and
we depict the Seifert shells that come from the algorithm.
Example 12 is known to be a 3 twist spun trefoil.
In our paper, we show that the surface bounds a
3-manifold that is a (3,1) Lens space
connected sum with 3 copies of the cartesean product
of a sphere and a circle.
J. Scott Carter
Department of Mathematics and Statistics
University of South Alabama
Mobile, Alabama 36688
Business telephone: (334)-460-6264
Fax: ( 334)-460-7969