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Published September 2018 | Submitted
Journal Article Open

The complexity of topological group isomorphism

Abstract

We study the complexity of the topological 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 Borel 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.

Additional Information

© 2018 The Association for Symbolic Logic. Published online: 23 October 2018. The first author was partially supported by NSF grant DMS 1464475. The second author was partially supported by the Marsden fund of New Zealand. The third author was supported by Sonderforschungsbereich 878 at Universität Münster.

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