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The Geometry and Topology of 3-Manifolds and Gravity

J. Gegenberg·G. Kunstatter
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Abstract

It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory in 2-D. I will show that a similar parameterization exists for 3-D Riemannian structures, with the conformal transformations and diffeomorphisms of the 2-D case replaced by a finite dimensional group of gauge transformations. This parameterization emerges from the theory of 3-D gravity coupled to topological matter.

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J. Gegenberg, G. Kunstatter. 1993-07-20. The Geometry and Topology of 3-Manifolds and Gravity. https://arxiv.org/abs/gr-qc/9307025

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