Generic isomorphism classes of abelian groups
Logic
2025-07-03 v2 General Topology
Group Theory
Abstract
We prove that the universal solenoid is the generic (in the sense of Baire category) connected compact metrizable abelian group. We also settle the dual problem in the sense of Pontryagin duality: , which is the dual of the universal solenoid, is the generic countably infinite torsion-free abelian group.
Cite
@article{arxiv.2306.05214,
title = {Generic isomorphism classes of abelian groups},
author = {Udayan B. Darji and Márton Elekes and Tamás Kátay and Anett Kocsis and Máté Pálfy},
journal= {arXiv preprint arXiv:2306.05214},
year = {2025}
}
Comments
13 pages