论文标题
Morse-Novikov的数字，隧道编号和缝合歧管的数量
Morse-Novikov numbers, tunnel numbers, and handle numbers of sutured manifolds
论文作者
论文摘要
从几何论证中开发出，从其隧道号来界定链接的莫尔斯 - 诺维科夫数量，我们在其沿表面的分解量的手柄上的缝合歧管$（m，γ）$（m，γ）$（m，γ）$（M，γ）$的上限上获得了上限和下限。固定缝合结构$（m，γ）$，这使我们开发了手柄号函数$ h \ colon H_2（m，\ partial m; \ mathbb {r}）\ to \ mathbb {n} $，它是界限的，在射线上是在射线上常数的，来自原点和本地最大。此外，对于整体级$ξ$，$ h（ξ）= 0 $，并且仅当沿某些表面的$（m，γ）$的分解为$ξ$是产品歧管。
Developed from geometric arguments for bounding the Morse-Novikov number of a link in terms of its tunnel number, we obtain upper and lower bounds on the handle number of a Heegaard splitting of a sutured manifold $(M,γ)$ in terms of the handle number of its decompositions along a surface representing a given 2nd homology class. Fixing the sutured structure $(M,γ)$, this leads us to develop the handle number function $h \colon H_2(M,\partial M;\mathbb{R}) \to \mathbb{N}$ which is bounded, constant on rays from the origin, and locally maximal. Furthermore, for an integral class $ξ$, $h(ξ)=0$ if and only if the decomposition of $(M,γ)$ along some surface representing $ξ$ is a product manifold.
