论文标题
焊接的扩展和限制图形移动
Welded extensions and ribbon restrictions of diagrammatical moves
论文作者
论文摘要
在本文中，我们考虑了字符串链路的经典和焊接图的本地移动，以及经典移动的焊接扩展的概念。这样的扩展通常不是唯一的，这个想法是找到一个可以将一个扩展与其他扩展隔离的拓扑标准。为此，我们转向$ \ mathbb {r}^4 $中的焊接字符串链接和打结的表面之间的关系，以及这些表面的功能区sublclass。这提供了对经典局部移动的拓扑解释，作为表面上的手术，以及焊接的局部移动作为色带表面上的手术。比较这些手术会导致经典局部移动的带状残留物的概念，我们表明，在某些广泛的条件下，最多可能有一种焊接延伸延伸，即带有带状残留物。但是，不能保证这种扩展的存在，我们提供反例。
In this paper, we consider local moves on classical and welded diagrams of string links, and the notion of welded extension of a classical move. Such extensions being non-unique in general, the idea is to find a topological criterion which could isolate one extension from the others. To that end, we turn to the relation between welded string links and knotted surfaces in $\mathbb{R}^4$, and the ribbon sublclass of these surfaces. This provides the topological interpretation of classical local moves as surgeries on surfaces, and of welded local moves as surgeries on ribbon surfaces. Comparing these surgeries leads to the notion of ribbon residue of a classical local move, and we show that up to some broad conditions there can be at most one welded extension which is a ribbon residue. The existence of such an extension is not guaranteed however, and we provide a counterexample.
