| Project/Area Number |
16540125
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Waseda University |
|---|
Principal Investigator |
EDA Katsuya Waseda University, Faculty of Science and Engineering, Professor (90015826)
|
|---|
| Project Period (FY) |
2004 – 2007
|
| Project Status |
Completed (Fiscal Year 2007)
|
| Budget Amount *help |
¥2,580,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥200,000 (Direct Cost: ¥200,000)
|
|---|
| Keywords | wild space / fundamental group / homotopy group / infinite words / compact abelian group / grope group / infinitary word / fundamental group / uncountable / non-commutative / wild space / Specker phenomenon |
|---|
| Research Abstract |
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.
|
