拟群的双数与欧拉示性数
Two-numbers and Euler characteristics for quandles
- Nara University of Education（奈良教育大学）
- Faculty of Environmental Studies, Hiroshima Institute of Technology（广岛工业大学环境学部）
- Department of Mathematics, Osaka Metropolitan University（大阪公立大学数学系）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究拟群版本陈-永野理论，探讨拟群的双数与欧拉示性数的关系，给出由交换群标记的有向简单图构造的有限拟群实例，验证或不验证对应对称空间的类似性质。
AI中文摘要：
拟群（quandles）可视为对称空间的推广。在陈省身（Chen）和永野（Nagano）发展的对称空间理论中，双数与欧拉示性数之间存在有趣的关联：双数是一种黎曼几何不变量，也可通过点对称性来刻画；欧拉示性数则是一种拓扑不变量。本文旨在启动拟群版本陈-永野理论的研究，特别探讨拟群的双数与欧拉示性数之间的关系，并提供有限拟群的例子，这些例子要么满足、要么不满足与对称空间性质类似的特性，这些例子由交换群标记的有向简单图构造而成。
英文摘要：
Quandles can be regarded as generalizations of symmetric spaces. In the theory of symmetric spaces developed by Chen and Nagano, there is an interesting relationship between the two-number and the Euler characteristic. The two-number is a Riemannian geometric invariant that can also be characterized in terms of point symmetries, whereas the Euler characteristic is a topological invariant. The aim of this paper is to initiate the study of quandle analogues of Chen--Nagano theory. In particular, we investigate relationships between the two-numbers and the Euler characteristics of quandles, and provide examples of finite quandles that either satisfy or fail to satisfy properties analogous to those of symmetric spaces. These examples are constructed from directed simple graphs labeled by abelian groups.
