论文标题
在有限类型的焊接弦链路和功能管
On finite type invariants of welded string links and ribbon tubes
论文作者
论文摘要
焊接打结的物体是结理论的组合扩展，可以用作研究$ 4 $空间的丝带表面的工具。 Kanenobu，Habiro和Shima开发了一种有限的色带打结表面理论，本文提出了使用焊接对象对这些不变的研究的研究。具体而言，我们研究了最高$ W_K $ - 等价的焊接链接链接，这是Yasuhara引入的等价关系，也是与有限类型理论有关的第二作者。在低度中，我们表明这种关系是有限类型不变性的信息。我们还研究了最大$ W_K $ - 等效性的焊接字符串链接的代数结构。所有结果均具有直接的色带打结表面的推论。
Welded knotted objects are a combinatorial extension of knot theory, which can be used as a tool for studying ribbon surfaces in $4$-space. A finite type invariant theory for ribbon knotted surfaces was developped by Kanenobu, Habiro and Shima, and this paper proposes a study of these invariants, using welded objects. Specifically, we study welded string links up to $w_k$-equivalence, which is an equivalence relation introduced by Yasuhara and the second author in connection with finite type theory. In low degrees, we show that this relation characterizes the information contained by finite type invariants. We also study the algebraic structure of welded string links up to $w_k$-equivalence. All results have direct corollaries for ribbon knotted surfaces.
