Embeddings of the line in the plane.
Embeddings of the line in the plane.
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DOI：
10.1515/crll.1982.337.113
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发表时间：
1982
期刊：
影响因子：
--
通讯作者：
L. Rudolph
中科院分区：
文献类型：
--
作者：
L. Rudolph
在文[1]中，Abhyankar和MoH证明了(直到代数自同构)特征为0的直线在平面上的唯一嵌入是标准嵌入。对于复数，这是一种很强的解结定理。本文仅利用纽结的一些合理的初等理论，给出了Abhyankar和Moh定理的一个新的证明；这个证明本质上是拓扑性的，而不仅仅是他们用“高中代数”的原始证明的翻译。
In their paper of this title [1], Abhyankar and Moh have shown that (up to algebraic automorphism) the only embedding of the line in the plane, in characteristic 0, is the Standard one. For the complex numbers, this is a strong sort of unknotting theorem. In this paper, using only some reasonably elementary theory of knots, I give a new proof of the theorem of Abhyankar and Moh; this proof is intrinsically topological, and does not appear merely to be a translation of their original proof using "high-school algebra".