| Project/Area Number |
24654013
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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 |
IWASE Norio 九州大学, 数理(科)学研究科(研究院), 教授 (60213287)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | Ａ∞構造 / Ａ∞圏 / Ａ∞作用 / 二分木 / 髭付き木 / A-infinity structure / tree construction / categorification / LS category / diffeology / Topos / associahedra / multiplihedra / Ａ∞関手 / Ａ∞代数 / Ａ∞空間 / 分類空間 / operad / A∞構造 / higher associativity / Associahedra / Multiplihedra / homotopy unit / strict unit / hopf unit |
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| Outline of Final Research Achievements |
I introduced small topological categories to abstract the essential ingredients from the notion of A-infinity structure to obtain its highly abstract definition, which is established in terms of category theory. I believe that the unit problem in A-infinity structure is resolved in positive by using this idea.
The main ingredients in the small topological categories are Associahedra and Multiplihedra and, in this research project, we enlarge a concrete description of the relationship between Associahedra and trivalent trees to another concrete description of the relationship between Multiplihedra and bearded trees using sequence of weights obtained from words spoken by the bearded trees.
This research program also offered an important view point to the study of L-S category, topological complexity and co-Hopf structure.
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