利用切割图进行组合链接同痕
Combinatorial link concordance using cut-diagrams
AI总结：
引入切割图概念，定义切割同痕关系，证明一维切割图的幂零周边系统是切割同痕不变量，并给出Stallings定理的组合版本。
摘要：
切割图是定义在1维和2维上的图解对象，推广了3维空间中的链环和4维空间中的曲面链环；在1维中，这与焊接链环理论一致。利用切割图，我们引入了一种称为切割同痕的等价关系，它包含了经典链环的拓扑同痕概念。我们的主要结果是，一维切割图的幂零周边系统是切割同痕的不变量，并在此过程中给出了Stallings定理的一个组合版本。我们还研究了与图解纽结理论中其他几个等价关系的关系，特别是与链环同伦的联系。
英文摘要：
Cut-diagrams are diagrammatic objects, defined in dimensions 1 and 2, that generalize links in 3-space and surface-links in 4-space; in dimension 1, this coincides with the theory of welded links. Using cut-diagrams, we introduce an equivalence relation called cut-concordance, which encompasses the topological notion of concordance for classical links. Our main result is that the nilpotent peripheral system of 1-dimensional cut-diagrams is an invariant of cut-concordance, giving along the way a combinatorial version of a theorem of Stallings. We also investigate the relationship with several other equivalence relations in diagrammatic knot theory, in particular in connection with link-homotopy.
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