The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity

Abstract

In this paper we describe the matter-free toroidal spacetime in 't Hooft's polygon approach to 2+1-dimensional gravity (i.e. we consider the case without any particles present). Contrary to earlier results in the literature we find that it is not possible to describe the torus by just one polygon but we need at least two polygons. We also show that the constraint algebra of the polygons closes.

18 pages Latex, 13 eps-figures

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Cited by in corpus (5)

• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Discrete structures in gravity
• (2+1) gravity for higher genus in the polygon model
• The polygon model for 2+1D gravity: the constraint algebra and problems of quantization
• 't Hooft's Polygon Approach Hyperbolically Revisited