Topology of the group of diffeomorphisms and the spaces of embeddings of manifolds

研究了纤维向球微分同构的光滑纤维束的分类问题。他定义了2维球上纤维束的“代数障碍”，并证明了如果纤维维数至少为7，如果障碍消失，则纤维束实际上是平凡的。他还证明了如果纤维的维数为5，并且如果障碍物消失，那么纤维束可以用2球的嵌入族和某个离散阿贝尔群的一个元素来表示。从而将球束的分类简化为一个代数问题和嵌入族的分类问题。

The author studied the classification problem of smooth fiber bundles with fiber diffeomorphic to the sphere. He defined "algebraic obstructions" for fiber bundles over 2-sphere with fiber diffeomorphic to odd dimensional sphere and showed that if the fiber dimension is at least 7 and if the obstructions vanish then the fiber bundle is in fact trivial. He also showed that if the fiber dimension is 5 and if the obstructions vanish then the fiber bundle is presentable by a family of embeddings of 2-spheres and an element of some discrete abelian group. Thus the classification of sphere bundles is reduced to an algebraic problem and the classification of families of embeddings.