 | Canonical Wick rotations in 3-dimensional gravity / Benedetti R., Bonsante F. - Providence: AMS, 2009. - viii, 164. - (Memoirs of the American Mathematical Society; Vol.198, N 926) - ISBN 978-0-8218-4281-2; ISSN 0065-9266
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Chapter 1. General view on themes and contents .................. 1
1.1. 3-dimensional constant curvature geometry .................. 2
1.2. Wick rotation and rescaling ................................ 2
1.3. Canonical cosmological time ................................ 3
1.4. Classification of flat globally hyperbolic spacetimes ...... 4
1.5. ML-spacetimes .............................................. 7
1.6. Canonical Wick rotations and rescalings ................... 10
1.7. Full classification ....................................... 11
1.8. The other side of Uλ-1 - (Broken) T-symmetry ............... 11
1.9. QD-spacetimes ............................................. 13
1.10.Along rays of spacetimes .................................. 14
1.11.QFT and ending spacetimes ................................. 15
Chapter 2. Geometry models ..................................... 23
2.1. Generalities on (X, G)-structures ......................... 23
2.2. Minkowski space ........................................... 24
2.3. De Sitter space ........................................... 25
2.4. Anti de Sitter space ...................................... 26
2.5. Complex projective structures on surfaces ................. 31
Chapter 3. Flat globally hyperbolic spacetimes ................. 35
3.1. Globally hyperbolic spacetimes ............................ 35
3.2. Cosmological time ......................................... 36
3.3. Regular domains ........................................... 37
3.4. Measured geodesic laminations on straight convex sets ..... 41
3.5. From measured geodesic laminations towards regular
domains ................................................... 46
3.6. From regular domains towards measured geodesic
laminations ............................................... 52
3.7. Initial singularities and  -trees ......................... 58
3.8. Equivariant constructions ................................. 59
Chapter 4. Flat Lorentzian vs hyperbolic geometry .............. 63
4.1. Hyperbolic bending cocycles ............................... 63
4.2. The Wick rotation ......................................... 69
4.3. On the geometry of Mλ ..................................... 74
4.4. Equivariant theory ........................................ 82
Chapter 5. Flat vs de Sitter Lorentzian geometry ............... 85
5.1. Standard de Sitter spacetimes ............................. 85
5.2. The rescaling ............................................. 86
5.3. Equivariant theory ........................................ 90
Chapter 6. Flat vs AdS Lorentzian geometry ..................... 93
6.1. Bending in AdS space ...................................... 93
6.2. Canonical AdS rescaling ................................... 99
6.3. Maximal globally hyperbolic AdS spacetimes ............... 102
6.4. Classification via AdS rescaling ......................... 111
6.5. Equivariant rescaling .................................... 116
6.6. AdS rescaling and generalized earthquakes ................ 117
6.7. T-symmetry ............................................... 122
6.8. Examples ................................................. 122
Chapter 7. QD-spacetimes ...................................... 127
7.1. Quadratic differentials .................................. 127
7.2. Flat QD-spacetimes ....................................... 129
7.3. QD Wick rotation-rescaling theory ........................ 134
Chapter 8. Complements ........................................ 145
8.1. Moving along a ray of laminations ........................ 145
8.2. More compact Cauchy surfaces ............................. 149
8.3. Including particles ...................................... 155
8.4. Open questions ........................................... 157
Bibliography .................................................. 159
Index ......................................................... 163
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