排序方式: 共有7条查询结果,搜索用时 15 毫秒
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P. V. Chernikov 《Mathematical Notes》2006,79(1-2):283-284
It is proved that a compact space is homotopy equivalent to a CW-complex if and only if it is an absolute neighborhood h-retract. 相似文献
2.
Deng Pin Liu 《数学学报(英文版)》2018,34(11):1742-1754
Let Pn be a simple n-polytope with a Z2-characteristic function λ. And h is a Morse function over Pn. Then the small cover Mn(λ) corresponding to the pair (Pn, λ) has a cell structure given by h. From this cell structure we can derive a cellular chain complex of Mn(λ) with integer coefficients. In this paper, firstly, we discuss the highest dimensional boundary morphism ∂n of this cellular chain complex and get that ∂n=0 or 2 by a natural way. And then, from the well-known result that the submanifold corresponding to (F, λF) is naturally a small cover with dimension k, where F is any k-face of Pn and λF is the restriction of λ on F, we get that ∂k=0 or ±2 for 0 ≤ k < n. Finally, by using the definition of inherited characteristic function which is the restriction of λ on the faces of Pn, we get a way to calculate the homology groups of Mn(λ). Applying our result to a 3-small cover we have that the homology groups of any 3-small cover is torsion-free or has only 2-torsion. 相似文献
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4.
Leonard R. Rubin Philip J. Schapiro 《Transactions of the American Mathematical Society》2006,358(6):2507-2536
We prove a -resolution theorem for simply connected CW- complexes in extension theory in the class of metrizable compacta . This means that if is a connected CW-complex, is an abelian group, , , for , and (in the sense of extension theory, that is, is an absolute extensor for ), then there exists a metrizable compactum and a surjective map such that:
(a) is -acyclic,
(b) , and
(c) .
This implies the -resolution theorem for arbitrary abelian groups for cohomological dimension when . Thus, in case is an Eilenberg-MacLane complex of type , then (c) becomes .
If in addition , then (a) can be replaced by the stronger statement,
(aa) is -acyclic.
To say that a map is -acyclic means that for each , every map of the fiber to is nullhomotopic.
5.
Hans-Joachim Baues 《K-Theory》1997,11(3):259-285
A category of homotopy pairs is characterised by a cohomology class which generalizes the notion of Toda bracket. Explicit computations of such cohomology classes are described. 相似文献
6.
Extension dimension is characterized in terms of -maps. We apply this result to prove that extension dimension is preserved by refinable maps between metrizable spaces. It is also shown that refinable maps preserve some infinite-dimensional properties. 相似文献
7.
Elton Pasku 《Semigroup Forum》2008,76(3):427-468
If a monoid S is given by some finite complete presentation ℘, we construct inductively a chain of CW-complexes
such that Δ
n
has dimension n, for every 2≤m≤n, the m-skeleton of Δ
n
is Δ
m
, and p
m
are critical (m+1)-cells with 1≤m≤n−2. For every 2≤m≤n−1, the following is an exact sequence of (ℤS,ℤS)-bimodules
where
if m=2. We then use these sequences to obtain a free finitely generated bimodule partial resolution of ℤS. Also we show that for groups properties FDT and FHT coincide. 相似文献
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