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Classification of the cohomology rings of finite Hopf spaces

有限Hopf空间上同调环的分类

基本信息

批准号：
11640083
负责人：
HEMMI Yutaka
金额：
$ 2.24万
依托单位：
KOCHI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640083/
关键词：
Hopf spaces iterated H-deviation Steenrod operations higher order operations quasi p-regular homotopy groups of spheres self homotopy equivalences Moore space mod p cohomology Moore space 同変ホモトピー

项目摘要

The summary of reserch results is as follows.1. We constructed p-th order mod p unstable cohomology operations for any odd prime p. Then, by using the operation, we studied the action of the Steenrod operations on the cohomology of the mod p finite Hopf spaces. We gave a lecture on a part of our resutl at the Japan-America Mathematics Institute at the Johns Hopkins University held at March 2000.2. In order to apply the above p-th order operation to the cohomology of Hopf spaces, we introduced iterated H-deviation for maps between Hopf spaces, which is an extension of the H-deviation.3. We studied conditions for mod p finite Hopf spaces to be quase p-regular. Our result is a considered as a generalization of the result by Kumpel for the p-regularity of mod p finite Hopf spaces. Our result includes the results by Harper, McClearly and Wilkerson.4. O^^-shima determined the group structure of the set of self homotopy equivalences for the exceptional group G_2. While Morisugi determined the one for the classical groups SU (3), Sp (2).5. Shimomura studied the υ^<-1>_2BP-localized homotopy groups of the spheres localized at prime 2 or 3. Komatsu studied orbit closure decompositions of tiling spaces by the generalized projection method. Tsukiyama studied the group of homotopy equivalence classes of S^1-bundles.

研究结果总结如下：1.对任意奇素数p构造了p阶mod p不稳定上同调算子，并利用该算子研究了Steenrod算子对mod p有限Hopf空间上同调的作用. 2000年3月，我们在约翰霍普金斯大学的日美数学研究所做了一次关于我们研究结果的演讲。为了将上述p阶运算应用于Hopf空间的上同调，我们对Hopf空间之间的映射引入了迭代H-偏差，它是H-偏差的推广。研究了mod p有限Hopf空间是拟p-正则的条件。我们的结果被认为是Kumpel关于mod p有限Hopf空间的p-正则性的结果的推广。我们的结果包含了哈珀，McClearly和Wilkerson的结果. O^^-shima确定了例外群G_2的自同伦等价集的群结构。而Morisugi确定了经典群SU（3），Sp（2）的一个。下村研究了<-1>定域为素数2或3的球面的π ^2BP-定域同伦群。Komatsu利用广义投影方法研究了平铺空间的轨道闭包分解。月山研究了S^1-丛的同伦等价类群。