Infinitely generated objects

无限生成的对象

基本信息

批准号：
16540125
负责人：
EDA Katsuya
金额：
$ 1.65万
依托单位：
Waseda University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2007
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16540125/
关键词：
wild space fundamental group homotopy group infinite words compact abelian group grope group infinitary word fundamental group uncountable non-commutative wild space Specker phenomenon

项目摘要

We have gotten results on the following five items. That is, we gotten considerably sufficient results for our original plans except for continuous words.(1) The fundamental groups of wild spaces ; (2) New constructions of wild spaces ; (3) A classification of finite-sheeted convering maps over 2-dimensional compact abelian groups ; (4) Grope groups ; (6) Infinitary words.(1): Suppose that a Peano continuum X is wild everywhere, i.e. not locally semi-simply connected at every point and pi_1(X) is a subgroup of the free product G^*H. Then, pi_1(X) is a conjugate of a subgroup of G or H. This implies that the fundamental groups of wild Peano continua cannot only be taken part into free products, but have a completely opposite property. This result was announced at the occasion of Borsuk conference and was submitted in December of 2005. This result is applied to a study of the fundamental groups obtained by attaching copies of the Hawaiian aearring to manifolds.(2) : In a collabolation with D. Repovs and U. Karimov we introduced a new construction of a space SC(X), which is obtained by attaching a cone C(X) to the square along the Topologists' sine curve. For a connected space SC(X) is simply-connected, and pi _2(4) is trivial if and only if pi_1(X) is trivial.

我们在以下五个项目上取得了结果。也就是说，除了连续的单词外，我们的原始计划取得了相当大的结果。（1）基本的野生空间群体；（2）野生空间的新结构；（3）在二维紧凑型阿伯利亚组上的有限分配的转换图的分类；（4）灰分组；（6）无限单词。（1）：假设Peano Continuum X到处都是野生的，即在每个点都不是局部半模拟连接，而PI_1（x）是自由产品G^*H的子组。然后，pi_1（x）是G或H子组的共轭物。这意味着野生Peano Continua的基本组不能仅仅参与免费产品，而是具有完全相反的特性。 This result was announced at the occasion of Borsuk conference and was submitted in December of 2005. This result is applied to a study of the fundamental groups obtained by attaching copies of the Hawaiian aearring to manifolds.(2) : In a collabolation with D. Repovs and U. Karimov we introduced a new construction of a space SC(X), which is obtained by attaching a cone C(X) to the square along the Topologists' sine 曲线。对于连接的空格SC（x），当且仅当PI_1（x）很琐碎时，PI _2（4）是微不足道的。