The Geometry and Topology of 3-Manifolds and Gravity

Details The Geometry and Topology of 3-Manifolds and Gravity The Geometry and Topology of 3-Manifolds and Gravity

1993-07-20

arxiv.org/abs/gr-qc/9307025v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, LateX

Scientific paper

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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