AI 中文总结
本文针对紧致平坦流形对上的仿射自映射，利用环境完整群与稳定化子完整群导出相对 Nielsen 数的显式公式，推广了既有结果，并指出稳定化子完整群不可被内蕴完整群替代。
AI 中文摘要
本文研究紧致平坦流形对上的仿射自映射。我们推导出相对 Nielsen 数的显式公式，该公式以环境完整群和提升子流形的稳定化子所承载的完整群来表达。该公式将 Wong 的幂零流形对公式的平坦特例推广至有限完整群情形，在平坦重叠区域与作者早先的模型-可解流形对公式一致，并进一步推广之。我们还证明，稳定化子完整群一般不能被替换为子流形的内蕴完整群。实例展示了有趣的 Schirmer 理论，并包含模型-可解流形类之外的平坦流形对。
英文摘要
In this paper we consider affine selfmaps of compact flat manifold pairs. We derive an explicit formula for the relative Nielsen number in terms of the ambient holonomy and the holonomy carried by the stabilizer of the lifted submanifold. The formula extends the flat specialization of Wong's nilmanifold-pair formula to finite holonomy, agrees with the author's earlier model-solvmanifold-pair formula on the flat overlap, and extends beyond it. We also show that the stabilizer holonomy cannot in general be replaced by the intrinsic holonomy of the submanifold. Examples exhibit interesting Schirmer theory and include flat pairs outside the model-solvmanifold class.
Comments16 pages
