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The Turaev genus of an adequate knot

机译：结的图拉耶夫属

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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-aiternating knot is of Turaev genus n. This is the first examples of adequate knots of Turaev genus two or more.
机译：结的图拉耶夫属是结交替的障碍。适当结是交替结的一般化。自然的问题是适当结的Turaev属的表征。在本文中，我们证明了适当的结的Turaev属是通过使用Khovanov同源性与结的适当图相关联的Turaev表面的属实现的。结果，我们获得了适当结的Turaev属的可加性，并表明适当结的Turaev属在突变下“经常”被保留。我们还证明了n个半交替的结是Turaev属n。这是图拉耶夫属两个或两个以上足结的第一个例子。

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