局部紧群中格的渐近不变量
群论
2022-10-31 v2 代数拓扑
动力系统
摘要
本工作的目的是理解固定局部紧群中格序列的一些渐近性质。特别地，我们将研究格的Betti数按余体积 renormalized 后的渐近增长，以及秩梯度（即按余体积 renormalized 的最小生成元个数）。为此，我们将考虑局部紧群在陪集空间上作用序列的超积，并展示其一个截面的性质如何与格的渐近性质相关联。
引用
@article{arxiv.1812.02133,
title = {Asymptotic invariants of lattices in locally compact groups},
author = {Alessandro Carderi},
journal= {arXiv preprint arXiv:1812.02133},
year = {2022}
}
备注
Final version, accepted in C. R. Math. Acad. Sci.. Major revision, many proofs were reworked and details were added. Most of Section 4 was rewritten. Minor changes to the main results