论文标题
链路中的表面标准位置在任意3曼if中的链接补充中
Standard position for surfaces in link complements in arbitrary 3-manifolds
论文作者
论文摘要
自1980年代以来，众所周知，交替的链路补充中的必需表面几乎可以横向到几乎到任何地方的链接图，除了某些良好的交叉点外，并因此在组合上进行了描述。这称为表面的标准位置，并且有许多应用。但是，原始技术仅适用于投影到3个球体内2个球员上的经典交替链接。在本文中，我们证明表面的标准位置可以扩展到更广泛的类别，即弱概括的交替链接。此类链接包括3个球员中的所有经典质量非分类交替链路，以及许多在较高属表面上交替的链接，或者除了三个球体以外的歧管。作为应用程序，我们表明所有此类链接都是主要的，并且在温和的限制下，与经典交替环境中的图相互作用的基本康威球体相互作用。
Since the 1980s, it has been known that essential surfaces in alternating link complements can be isotoped to be transverse to the link diagram almost everywhere, with the exception of some well-understood intersections, and described combinatorially as a result. This was called standard position for surfaces and has had numerous applications. However, the original techniques only apply to classical alternating links projected onto the 2-sphere inside the 3-sphere. In this paper, we prove that standard position for surfaces can be extended to a broader class, namely weakly generalized alternating links. Such links include all classical prime non-split alternating links in the 3-sphere, and also many links that are alternating on higher genus surfaces, or lie in manifolds besides the 3-sphere. As an application, we show that all such links are prime, and that under mild restrictions, essential Conway spheres for such links interact with the diagram exactly as in the classical alternating setting.
