Memoirs of the American Mathematical Society 2009; 164 pp; softcover Volume: 198 ISBN10: 0821842811 ISBN13: 9780821842812 List Price: US$72 Individual Members: US$43.20 Institutional Members: US$57.60 Order Code: MEMO/198/926
 The authors develop a canonical Wick rotationrescaling theory in \(3\)dimensional gravity. This includes (a) A simultaneous classification: this shows how maximal globally hyperbolic spacetimes of arbitrary constant curvature, which admit a complete Cauchy surface and canonical cosmological time, as well as complex projective structures on arbitrary surfaces, are all different materializations of "more fundamental" encoding structures. (b) Canonical geometric correlations: this shows how spacetimes of different curvature, that share a same encoding structure, are related to each other by canonical rescalings, and how they can be transformed by canonical Wick rotations in hyperbolic \(3\)manifolds, that carry the appropriate asymptotic projective structure. Both Wick rotations and rescalings act along the canonical cosmological time and have universal rescaling functions. These correlations are functorial with respect to isomorphisms of the respective geometric categories. Table of Contents  General view on themes and contents
 Geometry models
 Flat globally hyperbolic spacetimes
 Flat Lorentzian vs hyperbolic geometry
 Flat vs de Sitter Lorentzian geometry
 Flat vs AdS Lorentzian geometry
 \({\mathcal Q}{\mathcal D}\)spacetimes
 Complements
 Bibliography
 Index
