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 Surfaces " 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.

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J. Scott Carter
Department of Mathematics and Statistics
University of South Alabama
Mobile, Alabama 36688
U.S.A.
Business telephone: (334)-460-6264
Fax: ( 334)-460-7969
E-mail: carter@mathstat.usouthal.edu

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