Isotropy groups and group topologies (Q2474653)

Let \(S\) be a topological semigroup acting on a compact phase space. Consider the universal semigroup compactification of \(S\). It is known that the action of \(S\) can be extended to the compactification such that all minimal flows are flows isomorphic to quotients of the compactification via closed left congruences. One can also associate a subgroup of the maximal group in any minimal left ideal of the compactification to each minimal flow. These subgroups are referred to as isotropy groups in the literature and are important to tower constructions of minimal flows. In the paper alternative topologies on the maximal group where every closed subgroup in these topologies is an isotropy group for some minimal flow, are studied.