Compact Lie groups isolated up to conjugacy
Bal\'azs Csik\'os, Tam\'as K\'atay, Anett Kocsis, M\'at\'e P\'alfy

TL;DR
This paper characterizes compact subgroups of Lie groups that are isolated up to conjugacy, based solely on their intrinsic structure, and explores the properties of induced maps between subgroup spaces.
Contribution
It provides a characterization of isolated conjugacy classes of compact subgroups in Lie groups independent of embedding details.
Findings
Characterization depends only on the subgroup's intrinsic structure
Continuous homomorphisms induce open maps between subgroup spaces
Identification of isolated subgroups up to conjugacy in Lie groups
Abstract
The set of compact subgroups of a Hausdorff topological group can be equipped with the Vietoris topology. A compact subgroup is isolated up to conjugacy if there is a neighborhood of such that every is conjugate to . In this paper, we characterize compact subgroups of a Lie group that are isolated up to conjugacy. Our characterization depends only on the intrinsic structure of , the ambient Lie group and the embedding of into are irrelevant. In addition, we prove that any continuous homomorphism from a compact group onto a compact Lie group induces a continuous open map from onto .
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Taxonomy
TopicsAdvanced Topology and Set Theory · Homotopy and Cohomology in Algebraic Topology
