Year: 2024
Type: preprint
Abstract: A Riemannian manifold is a called a good rational expander in dimension $i$ if every $i$-cycle bounds a rational $i+1$-chain of comparatively small volume. We construct 3-manifolds which are good expanders in all dimensions. On the other hand, we show that expanders must be topologically complicated: they must have lots of torsion homology. We also give some applications to topological overlap problems, constructing examples of 3-manifolds with large width over $\mathbb R^2$.
Source: arXiv (Cornell University)
Author: Zung, Jonathan
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4396816419