2011 Fiscal Year Final Research Report
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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| Keywords | 位相幾何 |
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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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Research Products
(17 results)
