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NON-TRIVIAL REALIZATIONS OF VIRTUAL LINK DIAGRAMS

H. A. DYE

MADN-MATH, United States Military Academy, 646 Swift Road, West Point, NY 10996, USA

https://doi.org/10.1142/S0218216506004890Cited by:1 (Source: Crossref)

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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