Finitely cyclic homogeneous continua

Krupski, Paweł; Rogers, James T.

doi:10.1090/S0002-9939-1991-1062393-9

Finitely cyclic homogeneous continua
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by Paweł Krupski and James T. Rogers PDF

Proc. Amer. Math. Soc. 113 (1991), 1173-1177 Request permission

Abstract:

A curve is finitely cyclic if and only if it is the inverse limit of graphs of genus $\leq k$ , where $k$ is some integer. In this paper it is shown that if $X$ is a homogeneous finitely cyclic curve that is not tree-like, then $X$ is a solenoid or $X$ 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.

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