Consider the topological group(s) in https://en.wikipedia.org/wiki/Solenoid_(mathematics)#Pathological_properties
This seems like an interesting and bizarre group. It is obviously not a Lie group and obviously not a manifold. However, I was wondering if it satisfies geometric properties like local contractibility? What about its homology groups? Is there a nice reference for the topological properties of this group?
Could anyone tell me more about this group? Thanks!