论文标题
和弦图在球形曲线上的空间
Space of chord diagrams on spherical curves
论文作者
论文摘要
在本文中，我们给出了$ \ mathbb {z} $的定义 - 从$ \sum_iα_ix_i $表示的conterical/plane曲线的环境同位素类别中的有价值函数。然后，我们介绍由和弦图生成的免费$ \ mathbb {z} $ - 最多使用$ l $和弦生成的模块，称为（i）类型（（sii），（wii），（wii），（siii），（siii），或（wiii）或（wiii），或（wiii），或（wiii），spess。 $ \sum_iα_ix_i $。 The main result (Theorem~1) shows that if $\sum_i α_i \tilde{x}_i$ vanishes for the relators of Type (I) ((SII), (WII), (SIII), or (WIII), resp.), then $\sum_i α_i x_i$ is invariant under the Reidemeister move of type RI (strong RII, weak RII，强RIII或弱RIII，分别是[Ito-Takimura（2013），J。Knot Theory Ramifations]中定义的。
In this paper, we give a definition of $\mathbb{Z}$-valued functions from the ambient isotopy classes of spherical/plane curves derived from chord diagrams, denoted by $\sum_i α_i x_i$. Then, we introduce certain elements of the free $\mathbb{Z}$-module generated by the chord diagrams with at most $l$ chords, called relators of Type (I) ((SII), (WII), (SIII), or (WIII), resp.), and introduce another function $\sum_i α_i \tilde{x}_i$ derived from $\sum_i α_i x_i$. The main result (Theorem~1) shows that if $\sum_i α_i \tilde{x}_i$ vanishes for the relators of Type (I) ((SII), (WII), (SIII), or (WIII), resp.), then $\sum_i α_i x_i$ is invariant under the Reidemeister move of type RI (strong RII, weak RII, strong RIII, or weak RIII, resp.) that is defined in [Ito-Takimura (2013), J. Knot Theory Ramifications].
