2011 Fiscal Year Final Research Report
Toward Homotopy-Algebra Model using A-infinity Algebra
| Project/Area Number |
21654012
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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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, 数理学研究院, 教授 (60213287)
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| Project Period (FY) |
2009 – 2011
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| Keywords | A∞代数 / ホモトピー代数 / A∞圏 / 微分次数付き余代数 / 二重バー構成 / 単位元 / ホモトピー作用 |
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| Research Abstract |
There are two different definitions of A∞structures on a space, both are introduced by J. D. Stasheff. One requires a strict unit and the other requires only a homotopy unit. We give a proof for that an A∞space with homotopy unit is homotopy equivalent to an A∞space with strict unit. We also give a definition of a two-sided Borel construction for A∞actions, which must imply that no cohomological difference shall appear after deforming a true action as A∞action.
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