87 research outputs found
Homogeneous Transformation Groups of the Sphere
In this paper, we study the structure of homogeneous subgroups of the
homeomorphism group of the sphere, which are defined as closed groups of
homeomorphisms of the sphere that contain the rotation group. We prove two
structure theorems about the behaviour and properties of such groups and
present a diagram of the structure of these groups partly on the basis of these
results. In addition, we prove a number of explicit relations between the
groups in the diagram.Comment: This paper has been withdrawn by an irreconcilable difference of
opinion between the authors on its presentation and content
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