Representations of 3-manifolds and geometric informations derived from them

1. 3-流形的图解skobayashi利用Rubinstein-Scharlemann定义的图解给出了2-桥结外部的高度分裂的完整分类。利用结外缘局部检测heegard分裂的强不可约性。skobayashi和Yo'av Rieck分析了强不可约heegard分裂如何与3球中非平凡结的外缘相交，并证明了这种heegard表面与结外缘在子向环上相交。3 .森本猜想的研究kobayashi和Yo'av rieck研究了关于3流形中结的连通和和隧道数的森本猜想。4 . heegard分裂的附加同胚分解为Dehn扭转的算法sochiai给出了将属2 heegard分裂的给定附加同胚分解为标准Dehn扭转的算法。skatagiri通过Ricci曲率研究了黎曼泛函，并证明了爱因斯坦度规是该泛函的一个临界点，但也存在非爱因斯坦度规的临界点。他还给出了临界点为爱因斯坦度量的充分条件。

1. Graphic of 3-manifoldsKobayashi make use of the graphic defined by Rubinstein-Scharlemann to give a complete classification of Heegaard splittings of the exteriors of the 2-bridge knots.2. Local detection of strong irreducibility of Heegaard splittings by using knot exteriorsKobayashi together with, Yo'av Rieck analyzed how strongly irreducible Heegaard splittings can intersect the exteriors of non-trivial knots in the 3-sphere and showed that such Heegaard surface intersect the knot exteriors in meridional annuli.3. Research on Morimoto's ConjectureKobayashi together with Yo'av Rieckstudied about Morimoto's Conjecture concerned with the connectedsums of knots in 3-manifolds and the tunnel numbers.4. Algorithm for decompositions of attaching homeomorphisms of Heegaard splittings into Dehn twistsOchiai gave an algorithm for giving a decomposition of given attaching homeomorphisms of genus two Heegaard splittings into standard Dehn twists.5. Moduli space of metrics of Riemannian manifoldsKatagiri studied about Riemannian functional via Ricci curvature and showed that Einstein metric is a critical point of this functional, however there exist critical points that are not Einstein metric. He also gave a sufficient condition for critical points to be Einstein metrics.