Lifting Surface Automorphisms in ℝ3 to S3
Jane Gilman · 2024
Every compact oriented Riemann surface S with a finite group G of selfhomeomorphism can be embedded conformally in Euclidean three-space R 3 so that the image group acts conformally. Here we establish necessary and sufficient conditions on the fixed point structure as given by Harvey’s surface kernel map for the image group to lift to S 3 , the three-sphere, Corollary 5.6. This builds upon topological work of Ni, Wang, and Wang [24]. This new result gives rise to a discussion: how terms emerge and are used for equivalent phenomena that are described in the language of different fields.