Characteristic classes of surface bundles
Characteristic classes of surface bundles
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DOI：
10.1090/s0273-0979-1984-15321-7
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发表时间：
1984-10
影响因子：
3.1
通讯作者：
S. Morita
中科院分区：
文献类型：
--
作者：
S. Morita
设M是C~-流形.若要对流形上所有以M为纤维的可微纤维丛进行分类，则必须研究相应的结构群DiffM的拓扑，DiffM是M的所有带C ~拓扑的单同态的群。很容易看出Diff M的恒等式的连通分支Diffo M是开子群。因此，商群@（M）= Diff M/Diffo M上的自然拓扑是离散拓扑。因此我们有纤维化
Let M be a C~-manifold. If one wants to classify all differentiable fibre bundles over a given manifold which have M as fibres, then one must study the topology of the corresponding structure group DiffM, the group of all diffeomorphisms of M equipped with the C ~ topology. It is easy to see that the connected component Diffo M of the identity of Diff M is an open subgroup. Therefore the natural topology on the quotient group @(M)= Diff M/Diffo M, the diffeotopy group of M, is the discrete topology. Hence we have a fibration