On the top-dimensional $L^2$-Betti number of residually poly-$\mathbb Z$ groups
Abstract
Let $G$ be a residually poly-$\mathbb Z$ group of finite type. We prove that $G$ admits a poly-$\mathbb Z$ quotient with kernel $N$ satisfying $\mathrm{cd}_{\mathbb Q}(N) < \mathbb{cd}_{\mathbb Q}(G)$ if and only if the top-dimensional $L^2$-Betti number of $G$ vanishes.
Fields of Study & Subjects
Advanced Operator Algebra Research
Geometric and Algebraic Topology
Finite Group Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 26 January 2026
- Document type
- Preprint