论文标题
财产G和$ 4 $ - 属
Property G and the $4$--genus
论文作者
论文摘要
我们说，如果关于Thurston Norm的物业和$ K $的补充的纤维，则在$ 3 $ 3 $中的无原样结$ k $ - 歧管$ y $具有财产G，在$ k $的零手术下保留了$ k $的纤维。在本文中，我们将证明，如果$ 4 $ - $ k \ times \ {0 \} $（在某个同源性类中）中的$（y \ times [0,1]）\＃n \ edlline {\ mathbb cp^2 $ 4 $ - 属为$ 0 $，$ y $可以被视为任何封闭的，导向$ 3 $ - 歧管。
We say a null-homologous knot $K$ in a $3$--manifold $Y$ has Property G, if the properties about the Thurston norm and fiberedness of the complement of $K$ is preserved under the zero surgery on $K$. In this paper, we will show that, if the smooth $4$--genus of $K\times\{0\}$ (in a certain homology class) in $(Y\times[0,1])\#N\overline{\mathbb CP^2}$, where $Y$ is a rational homology sphere, is smaller than the Seifert genus of $K$, then $K$ has Property G. When the smooth $4$--genus is $0$, $Y$ can be taken to be any closed, oriented $3$--manifold.
