无理环面的差空间与算术
数学物理
2026-01-05 v3 math.MP
摘要
无理环面最初作为准晶体的几何模型引入，是微分空间理论中的一个基础对象。本文在回顾其主要代数性质后，对这一奇异空间的一个新几何不变量——流群——进行了全面分析。该不变量对所有流形都是平凡的，它作为微分空间背景下德拉姆定理障碍的核心而出现。我们提供了该群的完整计算和几何解释，证明了同构。
引用
@article{arxiv.2508.07460,
title = {Diffeology and Arithmetic of Irrational Tori},
author = {Patrick Iglesias-Zemmour},
journal= {arXiv preprint arXiv:2508.07460},
year = {2026}
}
备注
25 pages, 2 figures. This paper introduces a new geometric invariant, the group of flows, which is specific to diffeology as it is identically trivial for all manifolds. We provide the complete theory and a detailed application to the irrational torus, revealing a deep connection to arithmetic (fixed two misprints an improved a piece of proof)