A virtual link may be defined as an equivalence class of diagrams, or alternatively as a stable equivalence class of links in thickened surfaces. We prove that a minimal crossing virtual link diagram has minimal genus across representatives of the stable equivalence class. This is achieved by constructing a new parity theory for virtual links. As corollaries, we prove that the crossing, bridge, and ascending numbers of a classical link do not decrease when it is regarded as a virtual link. This extends corresponding results in the case of virtual knots due to Manturov and Chernov.

中文翻译：

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最小交叉数意味着最小支持属

虚拟链接可以定义为图的等价类，或者定义为加厚表面中链接的稳定等价类。我们证明了最小交叉虚拟链接图在稳定等价类的代表之间具有最小属。这是通过为虚拟链路构建新的奇偶校验理论来实现的。作为推论，我们证明了经典链路的交叉数、桥数和上升数在将其视为虚拟链路时不会减少。由于 Manturov 和 Chernov，这扩展了在虚拟结的情况下的相应结果。