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Non-Trivial Realizations of Virtual Link Diagrams

H. A. Dye
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Abstract

A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link diagram on an oriented 2-dimensional surface.) We prove that if a minimal genus representation meets certain criteria then there is a minimal genus representation resulting in a knotted realization.

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H. A. Dye. 2005-02-23. Non-Trivial Realizations of Virtual Link Diagrams. https://arxiv.org/abs/math/0502477

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