The complexity of topological group isomorphism
Logic
2021-08-24 v2 Group Theory
Abstract
We study the complexity of the isomorphism relation for various classes of closed subgroups of the group of permutations of the natural numbers. We use the setting of Borel reducibility between equivalence relations on Polish spaces. For profinite, locally compact, and Roelcke precompact groups, we show that the complexity is the same as the one of countable graph isomorphism. For oligomorphic groups, we merely establish this as an upper bound, which is not sharp because the relation is Borel.
Cite
@article{arxiv.1705.08081,
title = {The complexity of topological group isomorphism},
author = {Alexander S. Kechris and Andree Nies and Katrin Tent},
journal= {arXiv preprint arXiv:1705.08081},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:1604.00609