Finitely cyclic homogeneous continua

Abstract

A curve is finitely cyclic if and only if it is the inverse limit of graphs of genus ≤ k \leq k , where k k is some integer. In this paper it is shown that if X X is a homogeneous finitely cyclic curve that is not tree-like, then X X is a solenoid or X X admits a decomposition into mutually homeomorphic, homogeneous, tree-like continua with quotient space a solenoid. Since the Menger curve is homogeneous, the restriction to finitely cyclic curves is essential.