On indecomposable 1/2-homogeneous circle-like continua

摘要

We exhibit an indecomposable 1/2-homogeneous circle-like continuum, answering a question of Neumann-Lara, Pellicer-Covarrubias and Puga-Espinosa from 2005. Our solenoidal construction is an extension of Jim Rogers' proof of homogeneity of solenoids of pseu-doarcs and leads in turn to an uncountable family of mutually nonequivalent examples. In addition we prove that for an indecomposable 1/2 -homogeneous continuum Y the two orbits of Homeo(Y) are uncountable.