UNIVERSAL SPACES OF TWO-CELL COMPLEXES AND THEIR EXPONENT BOUNDS
UNIVERSAL SPACES OF TWO-CELL COMPLEXES AND THEIR EXPONENT BOUNDS
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双细胞复合体的通用空间及其指数界
DOI：
10.1093/qmath/hai015
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发表时间：
2006
影响因子：
0.7
通讯作者：
J. Grbić
中科院分区：
文献类型：
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作者：
J. Grbić
设p2n +1是由一个（2n+1）细胞通过悬浮映射附着在一个2m球体上形成的双胞复合体。在同伦结合、同伦交换h空间的范畴中构造了p2n +1的全称空间U。全称是指U是同伦结合的，同伦交换的，并且具有这样的性质：任何映射f: P 2n+1−→Y到一个同伦结合的，同伦交换的h空间Y扩展到一个唯一确定的h映射f: U−→Y。然后证明了U的h同伦指数的上界和下界。在模pr摩尔空间中，U是S上的pr幂映射的同伦纤维S{p}，我们得到了S{p}是同伦结合的、同伦交换的以及S{p}上的pr幂映射是零同伦的Neisendorfer的结论。数学学科分类（2000）：55P45, 55E15, 55Q70, 55P35
Let P 2n+1 be a two-cell complex which is formed by attaching a (2n+1)–cell to a 2m–sphere by a suspension map. We construct a universal space U for P 2n+1 in the category of homotopy associative, homotopy commutative H–spaces. By universal we mean that U is homotopy associative, homotopy commutative, and has the property that any map f : P 2n+1 −→ Y to a homotopy associative, homotopy commutative H–space Y extends to a uniquely determined H–map f : U −→ Y . We then prove upper and lower bounds of the H–homotopy exponent of U . In the case of a mod pr Moore space U is the homotopy fibre S{p} of the pr–power map on S, and we reproduce Neisendorfer’s result that S{p} is homotopy associative, homotopy commutative and that the pr–power map on S{p} is null homotopic. Mathematics Subject Classification (2000): 55P45, 55E15, 55Q70, 55P35