论文标题
Heegaard属，学位图和3个manifolds的合并
Heegaard genus, degree-one maps, and amalgamation of 3-manifolds
论文作者
论文摘要
令$ m = w \ cup_t v $是沿着圆环的两个紧凑的3个manifolds的融合，其中$ w $是同源球体中一个结的外部。让$ n $是通过用坚固的圆环代替$ w $获得的多种流形，以使$ w $中的塞弗特表面的边界是固体圆环的子午线。这意味着有一个学位的地图$ f \ colon m \ to n $，在修复$ v $的同时将$ w $捏成坚固的圆环。我们证明$ g（m）\ ge g（n）$，其中$ g（m）$表示Heegaard属。直接推论的是，卫星结的隧道数量至少与其图案结的隧道数量一样大。
Let $M=W\cup_T V$ be an amalgamation of two compact 3-manifolds along a torus, where $W$ is the exterior of a knot in a homology sphere. Let $N$ be the manifold obtained by replacing $W$ with a solid torus such that the boundary of a Seifert surface in $W$ is a meridian of the solid torus. This means that there is a degree-one map $f\colon M\to N$, pinching $W$ into a solid torus while fixing $V$. We prove that $g(M)\ge g(N)$, where $g(M)$ denotes the Heegaard genus. An immediate corollary is that the tunnel number of a satellite knot is at least as large as the tunnel number of its pattern knot.
