Universal spaces of two-cell complexes and their exponent bounds

被引:6
|
作者
Grbic, Jelena [1 ]
机构
[1] Univ Aberdeen, Dept Math Sci, Aberdeen AB24 3UE, Scotland
来源
QUARTERLY JOURNAL OF MATHEMATICS | 2006年 / 57卷
关键词
D O I
10.1093/qmath/hai015
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let P2n+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 P2n+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: P2n+1 -> Y to a homotopy associative, homotopy commutative H-space Y extends to a uniquely determined H-map fmacr: U -> Y. We then prove upper and lower bounds of the H-homotopy exponent of U. In the case of a mod p(r), Moore space U is the homotopy fibre S2n+1{p(r)} of the p(r)-power map on S2n+1, and we reproduce Neisendorfer's result that S2n+1{p(r)} is homotopy associative, homotopy commutative and that the p(r)-power map on S2n+1{p(r)} is null homotopic.
引用
收藏
页码:355 / 366
页数:12
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