No surface-knot of genus one has triple point number two
A. Al Kharusi, T. Yashiro
TL;DR
This paper proves that no genus-one surface-knot can have a triple point number of two, extending previous results about 2-knots and employing Roseman moves and algebraic intersection numbers.
Contribution
It introduces a proof that no genus-one surface-knot has triple point number two, expanding the understanding of surface-knot singularities.
Findings
No genus-one surface-knot has triple point number two.
The proof uses Roseman moves and algebraic intersection theory.
Extends known results from 2-knots to genus-one surface-knots.
Abstract
It is known that there is no 2-knot with triple point number two. The present work shows that there is no surface-knot of genus one with triple point number two. In order to prove the result, we use Roseman moves and the algebraic intersection number of simple closed curves in the double decker set.
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Taxonomy
TopicsGeometric and Algebraic Topology · Computational Geometry and Mesh Generation · Advanced Numerical Analysis Techniques