Homotopy theoretical research of manifolds

(1) Ishimoto研究了在亚稳范围内具有附加q柄的m球初等流形是否符合庞加莱猜想的问题。为此，他打算将James-Whitehead定理推广到初等流形定理，并在这种情况下成功地使区分初等流形的二次型在循环群中取值。利用这个结果，他在几乎所有的情况下，加上已经得到的结果，证明了当环群Z_<24>时，所讨论的问题也成立。(2) Fujioka研究了调和逆平均曲率曲面的基本性质，它是常平均曲率曲面的自然推广。特别是，他把这样的曲面描述为一个允许变换的曲面，它保留了用曲率表示的一定量。他还研究了庞内表面。(3) Tomari研究了滤波环的多重性理论，作为应用，他利用坐标的权值和Taylor展开构造了f的Milnor数的判据公式，给出了超曲面孤立奇点的定义。(4) Morishita在链路群与伽罗瓦群类比的基础上，研究了结点与素数、3流形与数域之间的类比关系，试图在代数数论与三维拓扑之间架起桥梁。他还在多伦多师从Murasugi。(5) Sugano研究了数论中3次酉群上的自同构形式。他用原始函数给出了爱森斯坦级数和库德拉升像的显式展开式，并给出了库德拉升在周期方面的不消失条件。

(1) Ishimoto studied the problem whether the matter corresponding to the Poincare conjecture holds or not for primary manifolds which are m-spheres with attached q-handles in the metastable range. For that purpose, he intended to extend the James-Whitehead theorem to the one for primary manifolds and succeeded in such case that the quadratic forms which distinguish primary manifolds take values in a cyclic group. Using the result, he proved in almost all cases that the matter in question also valid when the cyclic group is Z_<24>, adding to the results already obtained.(2) Fujioka studied the fundamental properties of harmonic inverse mean curvature surfaces which are natural generalization of constant mean curvature surfaces. In particular, he characterized such a surface as the one which admits a transformation preserving a certain quantity represented with curvature. He studied also the Bonnet surfaces.(3) Tomari studied the theory of multiplicity of filtered rings, and as an application, he constructed a criterion formula for the Milnor number of f which gives the definition of hyper surface isolated singularities, using the weight of coordinates and the Taylor expansion.(4) Morishita studied analogies between knots and primes, 3-manifolds and number fields, basing on the analogy between link groups and Galois groups, and tried to bridge between the algebraic number theory and the 3-dimensional topology. He also studied with K, Murasugi in Toronto.(5) Sugano studied the automorphic forms on unitary groups of degree 3 in number theory. He gave the explicit expansion for Eisenstein series and Kudla lift images using primitive theta functions, and gave the non-vanishing condition for the Kudla lift in terms of the periods.