A virtual link can be understood as a link in a trivial I-bundle over anorientable compact surface with genus. A twisted virtual link is a link in atrivial I-bundle over a not-necessarily orientable compact surface. A twistedvirtual birack is an algebraic structure with axioms derived from the twistedvirtual Reidemeister moves. We extend a method previously used with racks andbiracks to the twisted case to define computable invariants of twisted virtuallinks using finite twisted virtual biracks with birack rank $N\ge 1$. As anapplication, we classify twist structures on the virtual Hopf link.
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机译：虚拟链接可以理解为具有属的可定向紧致表面上的琐碎I束中的链接。扭曲的虚拟链接是在不必要的紧凑型曲面上的I形束中的链接。扭转虚拟机架是具有扭转虚拟Reidemeister运动的公理的代数结构。我们将先前用于机架和书架的方法扩展到扭曲的情况，以使用具有机架等级$ N \ ge 1 $的有限扭曲的虚拟机架定义扭曲的虚拟链接的可计算不变量。作为一种应用程序，我们对虚拟Hopf链接上的扭曲结构进行分类。
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