论同调挠率增长
几何拓扑
2022-12-16 v3 代数拓扑
群论
数论
摘要
我们证明了关于合适的算术格、Artin群和映射类群的高阶挠同调增长的新消失结果。该增长沿Farber序列理解，特别地，沿剩余链理解。对于主同余子群，我们还获得了挠率增长的强渐近界。作为核心工具，我们引入了一种称为有效重建的定量同伦方法。该方法构造有限指数子群的小分类空间，同时控制同伦的复杂性。该方法易于应用于自由阿贝尔群，并递归地扩展至广泛的剩余有限群类。
引用
@article{arxiv.2106.13051,
title = {On homology torsion growth},
author = {Miklos Abert and Nicolas Bergeron and Mikolaj Fraczyk and Damien Gaboriau},
journal= {arXiv preprint arXiv:2106.13051},
year = {2022}
}
备注
51 pages, 3 figures. Modifications after referee's recommandations. A section added of "1.3-speculations and questions" relating the homology growth with the sofic entropy Betti numbers. Name change: Right-angled groups become Chain-commuting groups (see Note 1, p. 8). Comments and a new reference added for the proof of Proposition 10.15 that was incomplete. To be published in J. Eur. Math. Soc