Classification of 3-manifolds by link correspondence and knot theory

建立了由闭连通的定向3流形集到素数连杆集和由素数连杆集到积分格点的δ集的正则对应关系，完成了长度不超过7的积分格点的对应分类。通过与博士的合作。Tayama，我们完成了从长度为8,9,10的素数链的集合到积分格点的集合的对应分类。在Reni-Mecchia-Zimmermann猜想上，首席研究员肯定地解决了这个猜想。此外，首席研究员估计了一个表面结的三点抵消数，并构造了一个表面结的三点抵消数和三点数之间有足够大差异的例子。

For our establishing canonical correspondences from the set of closed connected oriented 3-manifolds to the set of prime links and from the set of prime links to the delta set of integral lattice points, we completed the correspondence classifications for the integral lattice points of lengths up to 7. By joint works with Dr.I.Tayama, we completed the correspondence classification from the set of the prime links of lengths 8,9,10 to the delta set of integral lattice points. On Reni-Mecchia-Zimmermann's conjecture, the head investigator solved this conjecture affirmatively. Also, the head investigator estimated the triple point canceling number of a surface-knot and constructed an example of surface-knots with a sufficiently large difference between the triple point canceling number and the triple point number.