Acknowledgements ................................................ v
Chapter 1. Introduction ......................................... 1
Chapter 2. The orbit space ...................................... 5
2.1. Symplectic form on the T-orbits ............................ 5
2.2. Stabilizer subgroup classification ......................... 6
2.3. Orbifold structure of M/T .................................. 8
2.4. A flat connection for the projection M → M/T .............. 11
2.5. Symplectic tube theorem ................................... 12
Chapter 3. Global model ........................................ 15
3.1. Orbifold coverings of M/T ................................. 15
3.2. Symplectic structure on M/T ............................... 16
3.3. Model of (M, σ): Definition ............................... 17
3.4. Model of (M, σ): Proof .................................... 19
Chapter 4. Global model up to equivariant diffeomorphisms ..... 25
4.1. Generalization of Kahn's theorem .......................... 25
4.2. Smooth equivariant splittings ............................. 25
4.3. Alternative model ......................................... 28
Chapter 5. Classification: Free case ........................... 31
5.1. Monodromy invariant ....................................... 31
5.2. Uniqueness ................................................ 35
5.3. Existence ................................................. 38
5.4. Classification theorem .................................... 40
Chapter 6. Orbifold homology and geometric mappings ............ 43
6.1. Geometric torsion in homology of orbifolds ................ 43
6.2. Geometric isomorphisms .................................... 44
6.3. Symplectic and torsion geometric maps ..................... 46
6.4. Geometric isomorphisms: Characterization .................. 46
Chapter 7. Classification ...................................... 51
7.1. Monodromy invariant ....................................... 51
7.2. Uniqueness ................................................ 54
7.3. Existence ................................................. 55
7.4. Classification theorem .................................... 59
Chapter 8. The four-dimensional classification ................. 61
8.1. Two families of examples .................................. 61
8.2. Classification statement .................................. 62
8.3. Proof of Theorem 8.2.1 .................................... 64
8.4. Corollaries of Theorem 8.2.1 .............................. 69
Chapter 9. Appendix: (sometimes symplectic) orbifolds .......... 71
9.1. Bundles, connections ...................................... 71
9.2. Coverings ................................................. 72
9.3. Differential and symplectic forms ......................... 75
9.4. Orbifold homology, Hurewicz map ........................... 75
9.5. Classification of orbisurfaces ............................ 76
9.1. Bibliography .............................................. 79
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