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

研究了纤维与球面同构的光滑纤维丛的分类问题。他定义了“代数障碍”的纤维束2球与纤维同构奇数维领域，并表明，如果纤维的维度至少是7，如果障碍消失，然后纤维束实际上是平凡的。他还表明，如果纤维尺寸是5，如果障碍消失，然后纤维束是由一个家庭的嵌入2领域和一个元素的一些离散阿贝尔群。因此，球丛的分类被简化为一个代数问题和嵌入族的分类。

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.