2013 Fiscal Year Final Research Report
Structural Stability and Morphogenesis of Differentiable Maps
| Project/Area Number |
23654028
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Kyushu University |
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Principal Investigator |
SAEKI OSAMU 九州大学, マス・フォア・インダストリ研究所, 教授 (30201510)
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| Co-Investigator(Kenkyū-buntansha) |
OHMOTO Toru 北海道大学, 大学院・理学研究院, 教授 (20264400)
YAMAMOTO Takahiro 九州産業大学, 工学部, 講師 (60435972)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKASE Masamichi 成蹊大学, 理工学部, 准教授 (30447718)
YAMAMOTO Minoru 弘前大学, 教育学部, 准教授 (40435475)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 写像空間 / Vassiliev型不変量 / 映像理論 / 多値関数 / データ可視化 / 特異ファイバー |
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| Research Abstract |
The purpose of this research project was to formulate invariants of manifolds and maps from a new viepoint using a universal framework. For this, we considered Vassiliev complex for each classification of singularities or singular fibers and studied their invariants. Furthermore, we completely classified singular fibers of stable maps of 3-manifolds with boundary into the plane. We then calculated the cohomology groups of the associated Vassiliev complex and discovered new cobordism invariants. Moreover, we applied this kind of study to the visualization of multivariate data, and we showed that this kind of techniques can be very useful for clarifying differential topological features of a given set of big data.
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[Presentation] Desingularizing special generic maps2013
Author(s)
O. Saeki
Organizer
The 1st Franco-Japanese- Vietnamese Symposium on Singularities (and The 7th Franco-Japanese Symposium on Singularities)
Place of Presentation
Université de Nice Sophia Antipolis, France
Year and Date
2013-09-20
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