Infinitely generated objects

我们在以下五个项目上取得了成果。也就是说，我们得到了相当充分的结果，我们原来的计划，除了连续的话。(1)Wild空间的基本群;（2）Wild空间的新构造;（3）2维紧交换群上的有限片转换映射的分类;（4）Grope群;（6）无穷字。(1)假设Peano连续统X处处是Wild的，即不是在每一点上局部半单连通的，并且pi_1（X）是自由积G^*H的子群。则pi_1（X）是G或H的子群的共轭.这意味着，野皮亚诺连续统的基本群不仅不能参与自由积，而且具有完全相反的性质。这一结果是在Borsuk会议上宣布的，并于2005年12月提交。这一结果适用于研究的基本组附加副本的夏威夷aearring流形。(2)：与D. Repovs和U. Karimov等人提出了空间SC（X）的一种新的构造方法，它是在正方形沿着拓扑正弦曲线附加一个锥C（X）而得到的。对于连通空间SC（X）是单连通的，且pi_2（4）是平凡的当且仅当pi_1（X）是平凡的.

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.