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Twist Triviality of Canonical Seifert Surfaces

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Type
Preprint
Publication Date
Submission Date
Identifiers
arXiv ID: 1502.07582
Source
arXiv
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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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