A-infinity homotopy algebra and Hochshild homology

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654013
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Kyushu University
• Principal Investigator: IWASE Norio 九州大学, 数理(科)学研究科(研究院), 教授 (60213287)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: Ａ∞構造 / Ａ∞圏 / Ａ∞作用 / 二分木 / 髭付き木

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.

Free Research Field

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