In this talk, we discuss continuous orbit equivalence (coe for short) between two continuous group actions on compact spaces. Roughly speaking, this means there exists a homeomorphism between the spaces which identifies orbits on two sides continuously. We survey the known results on coe rigid actions, i.e. actions for which coe between them and other actions implies they are conjugate. Then we sketch the proof for a recent result on coe rigidity for minimal actions of infinite dihedral groups. Part of the talk is based on joint work with Nhan-Phu Chung.

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