Minimal crossing number implies minimal supporting genus

Will Rushworth (McMaster University)

We prove that a minimal crossing virtual link diagram is a minimal genus diagram. That is, the genus of its Carter surface realizes the supporting genus of the virtual link represented by the diagram. The result is obtained by introducing a new parity theory for virtual links. This answers a basic question in virtual knot theory, and recovers the corresponding result of Manturov in the case of virtual knots.
Joint work with Hans Boden.

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