The Cohomological Equation for Partially Hyperbolic Diffeomorphisms

Introduction 2 1. Techniques in the proof of Theorem A 7 2. Partial hyperbolicity and bunching conditions 10 2.1. Notation 11 3. The partially hyperbolic skew product associated to a cocycle 12 4. Saturated sections of admissible bundles 13 4.1. Saturated cocycles: proof of Theorem A, parts I and III 18 5. Hölder regularity: proof of Theorem A, part II. 21 6. Jets 28 6.1. Prolongations 29 6.2. Isomorphism of jet bundles 30 6.3. The graph transform on jets 30 7. Proof of Theorem B 33 8. Journé’s theorem, re(re)visited. 37 9. Saturated sections of partially hyperbolic extensions 50 9.1. Proof of Theorem A, Part IV from Theorem C 51 10. Tools for the proof of Theorem C 51 10.1. Fake invariant foliations 51 10.2. Further consequences of r-bunching 59 10.3. Fake holonomy 68 10.4. Central jets 73 10.5. Coordinates on the central jet bundle 75 10.6. Holonomy on central jets 77 10.7. Ec curves 80 11. Proof of Theorem C 83 12. Final remarks and further questions 92 Acknowledgments 92 References 92