论文标题
最小的交叉数意味着最小的支撑属
Minimal crossing number implies minimal supporting genus
论文作者
论文摘要
虚拟链接可以定义为图表的等效类别，也可以是稳定的对等链路中的稳定等效类别。我们证明，在稳定等效类别的代表中，最小的交叉虚拟链接图具有最小的属。这是通过为虚拟链接构建新的平价理论来实现的。作为推论，我们证明经典链接的交叉，桥和上升数量在被视为虚拟链接时不会减少。由于Manturov和Chernov，这在虚拟结中扩展了相应的结果。
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.
