摘要
定理给出了2维连通紧致曲面同胚的等价条件,这也是2维连通紧致曲面的分类问题。举例子表明了各维整下同调群同构的两拓扑空间未必同胚也未必同伦。最后应用归纳法和球状复形的Mayer-Vietoris序列得到n维实射影空间的各维整同调群。
Theorem 2 gives the equivalence conditions of the homeomorphism to two dimensional connected compact surface, which is also a classification problem of two dimensional connected compact surface. Example 1 shows that the two topological spaces are not homeomorphism and not homotopy, even if their whole homology group are isomorphism. Finally, using the induction and the Mayer-Vietoris sequence, we get the whole homology group.
出处
《江苏理工学院学报》
2017年第4期44-47,共4页
Journal of Jiangsu University of Technology
基金
国家自然科学基金(11471145)
关键词
同调群
同胚
同伦
同构
homology group
homeomorphism
homotopy
isomorphism
