The aim of the present project consists in detecting fundamental structures, which allow a unified understanding of low dimensional Riemannian and Lorentzian manifolds of constant curvature.
The point of view is that of Wick rotation-rescaling theory recently outlined by Benedetti and Bonsante. In this framework ends of geometrically finite hyperbolic manifolds support a natural Lorentzian metric for any fixed constant curvature.
The first objective is to investigate the relationships between classical ending invariants and these "ending spacetimes". This should provide a new insight in both hyperbolic geometry and gravity in dimension 3. On the other hand the Wick rotation-rescaling theory should be further extended in order to include the case of ends of an y complete hyperbolic 3-manifolds of finite type.
The present project falls within the timeline research area of 3D-gravity that has involved common efforts of both Mathematicians and Physicists in last years. Actually a deep motivation of the project is t o give a strong geometric support to recent 3D quantum field theories.
Call for proposal
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