自旋法向曲面的不可压缩准则
Incompressibility criteria for spun-normal surfaces
摘要：
本文给出了理想三角剖分中自旋法线曲面不可压缩的一个简单的充分条件，即它是一个在每个四面体中有一个四边形的非空边界顶点曲面。虽然这个条件是远远没有必要的，它是强大的，足以给两个新的结果：存在交替结与非整数边界斜率，并证明了斜率猜想的一大类2融合结。虽然条件和结论是纯粹的拓扑，证明使用的Culler-Shalen理论所产生的基本表面的理想点的字符品种，重新解释瑟斯顿和吉田。标准本身来自Kabaya的工作，我们将其放入正规曲面理论的语言中。这使得该标准很容易应用，并给出了证明该表面是不可压缩的框架。我们还探讨了自旋法线表面产生的变形品种的理想点。特别是，我们给出了一个例子，其中没有顶点或基本曲面以这种方式出现。
英文摘要：
We give a simple sufficient condition for a spun-normal surface in an ideal triangulation to be incompressible, namely that it is a vertex surface with non-empty boundary which has a quadrilateral in each tetrahedron. While this condition is far from being necessary, it is powerful enough to give two new results: the existence of alternating knots with non-integer boundary slopes, and a proof of the Slope Conjecture for a large class of 2-fusion knots. While the condition and conclusion are purely topological, the proof uses the Culler-Shalen theory of essential surfaces arising from ideal points of the character variety, as reinterpreted by Thurston and Yoshida. The criterion itself comes from the work of Kabaya, which we place into the language of normal surface theory. This allows the criterion to be easily applied, and gives the framework for proving that the surface is incompressible. We also explore which spun-normal surfaces arise from ideal points of the deformation variety. In particular, we give an example where no vertex or fundamental surface arises in this way.
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