Quandles and discrete symmetric spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654012
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Hiroshima University
• Principal Investigator: TAMARU Hiroshi 広島大学, 理学(系)研究科(研究院), 教授 (50306982)
• Co-Investigator(Renkei-kenkyūsha): AGAOKA Yoshio 広島大学, 大学院理学研究科, 教授 (50192894) ; SHIBUYA Kazuhiro 広島大学, 大学院理学研究科, 准教授 (00569832) ; KAMADA Seiichi 大阪市立大学, 大学院理学研究科, 教授 (60254380)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: カンドル / 対称空間 / 二点等質 / 平坦性

Outline of Final Research Achievements

We introduced the notion of two-point homogeneous quandles, which is an analogy of the notion of two-point homogeneous Riemannian manifolds, and classified those with finite cardinality (The prime cardinality case has been completed by the Principal Investigator, and other case by a Research Partner). We also defined the notion of flat quandles, and classified finite connected ones. The notion of flatness was not defined by curvatures, but a characterization of flat Riemannian symmetric spaces in terms of the transformation groups.

Free Research Field

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