Ininfitely generated objects(fundamental groups of wild spaces)
| Project/Area Number |
20540097
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Waseda University |
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Principal Investigator |
EDA Katsuya 早稲田大学, 理工学術院, 教授 (90015826)
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 位相幾何 / 基本群 / 野性的空間 / ハワイアンイヤリング / ホモロジー群 / コホモロジー群 / 連結 / 局所弧連結 / 1次元 / ホモトピー型 |
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| Research Abstract |
The central theme is the non-commutative Specker phenomenon, which is generic for uncountable groups. We studied it related to group theory and algebraic topology.
In particular we proved the following. The fundamental groups of Peano continua determine the homotopy types and each homomorphism between thosegroupsis essentially induced from a continuous map. In general the fundamental group of an arbirary Peano continuum cannot be decomposed into a non-trivial free product at wild parts. There exists a 2-dimensional, cell-like, simply-connected, non-contractible Peano continuum.
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Report
(5 results)
Research Products
(44 results)
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[Book] 内田老鶴圃2010
Author(s)
江田勝哉著
Total Pages
160
Publisher
数理論理学(使い方と考え方)
Related Report
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