The Turaev genus of an adequate knot
The Turaev genus of an adequate knot
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DOI：
10.1016/j.topol.2009.07.020
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发表时间：
2009-11
影响因子：
0.6
通讯作者：
Tetsuya Abe
中科院分区：
文献类型：
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作者：
Tetsuya Abe
纽结的图拉耶夫亏格是纽结交替的障碍。适当的纽结是交错纽结的推广。一个自然问题是一个充分纽结的图拉耶夫亏格的刻画。本文利用Khovanov同调证明了适当纽结的Turaev亏格是通过与纽结的适当图相联系的Turaev曲面亏格来实现的。作为结果，我们得到了适当纽结的Turaev亏格的可加性，并证明了适当纽结的Turaev亏格在突变下“经常”保持。我们还证明了n-半交错纽结属于Turaev亏格n，这是两个或更多个Turaev亏格的充分纽结的第一个例子。
The Turaev genus of a knot is an obstruction to the knot being alternating. An adequate knot is a generalization of an alternating knot. A natural problem is a characterization of the Turaev genus of an adequate knot. In this paper, we show that the Turaev genus of an adequate knot is realized by the genus of the Turaev surface associated to an adequate diagram of the knot using the Khovanov homology. As a result, we obtain the additivity of the Turaev genus of adequate knots, and show that the Turaev genus of an adequate knot is “often” preserved under mutation. We also show that an n-semi-alternating knot is of Turaev genus n. This is the first examples of adequate knots of Turaev genus two or more.