MOBIUS STRUCTURES AND TIMED CAUSAL SPACES ON THE CIRCLE

摘要

A conjectural duality is discussed between hyperbolic spaces on one hand and spacetimes on the other, living on the opposite sides of the common absolute. This duality goes via Miibius structures on the absolute, and it is easily recognized in the classical case of symmetric rank one spaces. In the general case, no trace of such duality is known. As a first step in this direction, it is shown how numerous Mobius structures on the circle, including those that stem from hyperbolic spaces, give rise to 2-dimensional spacetimes, which are axiomatic versions of de Sitter 2-space, and vice versa. The paper has two Appendices, one of which is written by V. Schroeder.