论文标题
古典和虚拟结的高阶有限类型不变型
Higher-order finite type invariants of classical and virtual knots and unknotting operations
论文作者
论文摘要
Vassiliev使用毫无打结的操作引入了打结的过滤不变性，称为交叉变化。 Goussarov，Polyak和Viro引入了虚拟结的其他过滤不变的，该顺序称为GPV-rorder，使用无结的操作称为虚拟化。我们定义了其他过滤不变的，该订单称为$ f $ order，使用未结的操作，称为“禁止移动”。在本文中，我们表明，$ f $ rorder $ \ le n+1 $的虚拟结一组严格强于$ f $ rorder $ \ le n $和gpv-rorder $ \ le 2n+1 $的虚拟结。为了获得结果，我们证明了$ f $ order $ \ le n $的虚拟结组包含gpv-rorder $ \ le 2n+1 $不变的每一个goussarov-polyak-viro，这意味着$ f $ - $ f $ ordore of $ f $ - 完整的classical of classical and virtlual knots of-f $ -
Vassiliev introduced filtered invariants of knots using an unknotting operation, called crossing changes. Goussarov, Polyak, and Viro introduced other filtered invariants of virtual knots, which order is called GPV-order, using an unknotting operation, called virtualization. We defined other filtered invariants, which order is called $F$-order, of virtual knots using an unknotting operation, called forbidden moves. In this paper, we show that the set of virtual knot invariants of $F$-order $\le n+1$ is strictly stronger than that of $F$-order $\le n$ and that of GPV-order $\le 2n+1$. To obtain the result, we show that the set of virtual knot invariants of $F$-order $\le n$ contains every Goussarov-Polyak-Viro invariant of GPV-order $\le 2n+1$, which implies that the set of virtual knot invariants of $F$-order is a complete invariant of classical and virtual knots.
