论文标题
交替的链接，理性球和立方体砖
Alternating links, rational balls, and cube tilings
论文作者
论文摘要
沿交替链路绑定有理同源球的交替链路的双球的双盖何时分支？ Heegaard Floer同源性为其绑定的必要条件提供了必要的条件：Link的棋盘晶格必须是立方体的，这意味着其归一化的决定因素小于或等于一个。我们猜想，当归一化的决定因素等于一个时，匡威会保留并证明它。证明涉及在平面图上的流动和hajós-minkowski定理，即欧几里得空间的晶格瓷砖包含一对沿整个方面的立方体。我们将主要结果扩展到了色带的研究和色带一致性的研究。
When does the double cover of the three-sphere branched along an alternating link bound a rational homology ball? Heegaard Floer homology generates a necessary condition for it to bound: the link's chessboard lattice must be cubiquitous, implying that its normalized determinant is less than or equal to one. We conjecture that the converse holds and prove it when the normalized determinant equals one. The proof involves flows on planar graphs and the Hajós-Minkowski theorem that a lattice tiling of Euclidean space by cubes contains a pair of cubes which touch along an entire facet. We extend our main results to the study of ribbon cobordism and ribbon concordance.
