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Twist Triviality of Canonical Seifert Surfaces

2015/02/26 by Michael Pfeuti, Pfeuti, Michael
Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.1502.07582

openalex publication_date 2015/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the idea of unknotting knots to Seifert surfaces. We define an operation called ribbon twist which serves as the equivalent of a crossing change for knots. A Seifert surface is considered untwisted, the equivalent to unknotted, if it is isotopic to a standardly embedded n-fold punctured torus. A Seifert surface is said to be twist trivial if it can be untwisted by ribbon twists. We show that canonical Seifert surfaces are twist trivial.

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