论文标题
HOPF学位定理的概括
A generalization of the Hopf degree theorem
论文作者
论文摘要
HOPF定理指出，从封闭式连接的平滑$ n $ -manifold $ m $到$ n $ sphere的连续地图的同型连续地图都是按其学位分类的。这样的地图等于$ n $ sphere捆绑包的一部分，超过$ m $。 HOPF定理的概括是针对超过$ m $的非平凡$ n $ sphere束的部分获得的。
The Hopf theorem states that homotopy classes of continuous maps from a closed connected oriented smooth $n$-manifold $M$ to the $n$-sphere are classified by their degree. Such a map is equivalent to a section of the trivial $n$-sphere bundle over $M$. A generalization of the Hopf theorem is obtained for sections of nontrivial oriented $n$-sphere bundles over $M$.
