On noncontractible compacta with trivial homology and homotopy groups
On noncontractible compacta with trivial homology and homotopy groups
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关于具有平凡同源和同伦群的不可收缩紧致
DOI：
10.1090/s0002-9939-09-10217-4
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Dušan D. Repovš
中科院分区：
文献类型：
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作者：
U. Karimov;Dušan D. Repovš
我们构造了一个Peano连续统X的例子，使得：（i）X是多面体的一点紧化;（ii）X是弱同伦等价于一点（即π n（X）对所有n > 0都是平凡的）;（iii）X是不可收缩的;（iv）X是同调和上同调局部连通的（即X是HLC和clc空间）。我们还证明了所有经典的同调群（奇异，切赫，和Borel-Moore），所有经典的上同调群（奇异和切赫），和所有有限维夏威夷群的X是平凡的。
We construct an example of a Peano continuum X such that: (i) X is a one-point compactification of a polyhedron; (ii) X is weakly homotopy equivalent to a point (i.e. π n (X) is trivial for all n > 0); (iii) X is noncontractible; and (iv) X is homologically and cohomologically locally connected (i.e. X is an HLC and clc space). We also prove that all classical homology groups (singular, Cech, and Borel-Moore), all classical cohomology groups (singular and Cech), and all finite-dimensional Hawaiian groups of X are trivial.