论文标题
增厚表面中交替链路的表征
A characterization of alternating links in thickened surfaces
论文作者
论文摘要
我们使用戈登 - 林地配对的扩展到增厚的表面，从而对变厚表面的交替链路进行拓扑表征。如果$σ$是封闭式的表面，而$ f $是$σ\ times i $的紧凑型表面，那么Gordon-Litherland配对将定义$ f $的第一个同源性对称的双线配对。如果其Gordon-Litherland配对是确定的形式，则$σ\ times i $中的紧凑型表面被称为确定。我们证明，在且仅当它界限两个确定的符号的表面时，在增厚表面中的非切片链接$ l $才能交替。
We use an extension of Gordon-Litherland pairing to thickened surfaces to give a topological characterization of alternating links in thickened surfaces. If $Σ$ is a closed oriented surface and $F$ is a compact unoriented surface in $Σ\times I$, then the Gordon-Litherland pairing defines a symmetric bilinear pairing on the first homology of $F$. A compact surface in $Σ\times I$ is called definite if its Gordon-Litherland pairing is a definite form. We prove that a non-split link $L$ in a thickened surface is alternating if and only if it bounds two definite surfaces of opposite sign.
