论文标题
Turaev属的极端Khovanov同源性附近
Near extremal Khovanov homology of Turaev genus one links
论文作者
论文摘要
链接图$ D $的Turaev表面是一个封闭的，定向的表面，该表面是由$ a $和$ d $的全$ a $和$ b $ thuffman状态之间的Coobordism构建的。 Link $ L $的Turaev属是任何图$ d $ l $的Turaev表面的最低属。当且仅当其Turaev属为零时，一个链接是交替的，因此人们可以将Turaev属的One链接视为与交替的链接接近。在本文中，我们研究了Turaev属的Khovanov同源性在第一和最后两个多项式等级中，同源性是非平凡的。我们表明，在Turaev属的Khovanov同源性中，一个链接的特殊求和是微不足道的。这个微不足道的求和导致了Rasmussen $ s $不变的计算，并在某些Turaev属的一节中界定了四个属的范围。
The Turaev surface of a link diagram $D$ is a closed, oriented surface constructed from a cobordism between the all-$A$ and all-$B$ Kauffman states of $D$. The Turaev genus of a link $L$ is the minimum genus of the Turaev surface of any diagram $D$ of $L$. A link is alternating if and only if its Turaev genus is zero, and so one can view Turaev genus one links as being close to alternating links. In this paper, we study the Khovanov homology of a Turaev genus one link in the first and last two polynomial gradings where the homology is nontrivial. We show that a particular summand in the Khovanov homology of a Turaev genus one link is trivial. This trivial summand leads to a computation of the Rasmussen $s$ invariant and to bounds on the smooth four genus for certain Turaev genus one knots.
