Contents
Introduction i x
Chapter 1. Geometri c natur e o f integrabilit y 1
1.1. Foliations , contac t structure s an d confoliation s 1
1.2. Dynamic s o f codimension on e foliation s 9
1.3. Plan e field s transversa l t o 1-dimensional bundle s 13
Chapter 2 . Perturbatio n o f confoliations int o contac t structure s 2 3
2.1. Linea r perturbation s 2 3
2.2. Conformally-Anoso v Flow s 2 4
2.3. Non-linea r deformation s 3 0
2.4. Approximation s o f foliations b y contac t structure s 3 1
2.5. Perturbatio n nea r holonom y curve s 3 1
2.6. Alternativ e approache s t o Propositio n 2.5. 1 3 6
2.7. Transitiv e confoliation s 3 7
2.8. Propagatio n o f the perturbatio n alon g the leave s 4 0
2.9. Discussio n 4 3
Chapter 3 . Tau t vs . Tigh t 4 5
3.1. Tigh t contac t structure s an d tau t foliation s 4 5
3.2. Symplecti c filling 4 6
3.3. Th e inequalit y 4 8
3.4. Contac t geometr y o f planes i n the standar d contac t R 3 5 1
3.5. Tigh t an d Tau t confoliation s 5 5
3.6. Homotop y o f confoliations 6 2
3.7. A few ope n problem s abou t confoliation s 6 3
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