Subdivision analysis of solutions to the Regge equations

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Abstract
Solutions to the Regge equations of motion in three dimensions are analyzed for the case of lens space topology. The behavior of the solutions under subdivision of the triangulations is studied in simplicial minisuperspace. In particular, we show that solutions which exist for one triangulation may disappear upon subdivision. We also find examples where solutions do not exist for a given triangulation, but do exist upon subdivision. Similar behavior is observed in four dimensions.