论文标题
一个强大的haken定理
A Strong Haken's Theorem
论文作者
论文摘要
假设t是一个可用于紧凑定向的3个manifold M的Heegaard拆分表面，而S是M。在1968年的Haken中，S haken表明，当时还有一个减少的球体S*用于Heegaard拆分。也就是说，s*是M的还原球，而表面t和s*在一个圆中相交。 1987年，卡森（Casson）和戈登（Gordon）将结果扩展到了M中的减边磁盘，并指出在这两种情况下，S*均通过S序列通过称为1个残酷的操作序列获得。在这里，我们表明实际上可能会服用S* =S。
Suppose T is a Heegaard splitting surface for a compact orientable 3-manifold M, and S is a reducing sphere for M. In 1968 Haken showed that there is then also a reducing sphere S* for the Heegaard splitting. That is, S* is a reducing sphere for M and the surfaces T and S* intersect in a single circle. In 1987 Casson and Gordon extended the result to boundary-reducing disks in M and noted that in both cases S* is obtained from S by a sequence of operations called 1-surgeries. Here we show that in fact one may take S* = S.
