Quadratic Isoperimetric Inequality for Mapping Tori of Free Group Automorphisms.

Intro -- Contents -- Abstract -- Introduction -- Acknowledgements -- Part 1. Positive Automorphisms -- 1.1. Van Kampen diagrams -- 1.2. Singularities and bounded cancellation -- 1.3. Past, future and colour -- 1.4. Strategy, strata and conditioning -- 1.5. Preferred futures, fast letters and cancellation -- 1.6. Counting non-constant letters -- 1.7. The bound on S0|A4(S0,)| and S0|A2(S0,)| -- 1.8. The pleasingly rapid consumption of colours -- 1.9. Teams and their associates -- 1.10. The Bonus Scheme -- 1.11. The proof of Theorem C -- 1.12. Glossary of constants -- Part 2. Train Tracks and the Beaded Decomposition -- 2.1. Improved relative train track maps -- 2.2. Hard splittings -- 2.3. A small reduction -- 2.4. Nibbled futures -- 2.5. Passing to an iterate of f -- 2.6. The nibbled futures of GEP s -- 2.7. Proof of the Beaded Decomposition Theorem -- 2.8. Refinements of the Beaded Decomposition Theorem -- Part 3. The General Case -- 3.1. The structure of diagrams -- 3.2. Adapting diagrams to the beaded decomposition -- 3.3. Linear bounds on the length of corridors -- 3.4. Replacing f by a suitable iterate -- 3.5. Preferred futures of beads -- 3.6. Counting fast beads -- 3.7. HNP-cancellation and reapers -- 3.8. Non-fast and unbounded beads -- 3.9. The pleasingly rapid disappearance of colours -- 3.10. Teams -- 3.11. The Bonus Scheme -- 3.12. From bead norm to length -- 3.13. Corridor length functions and bracketing -- 3.14. On a result of Brinkmann -- Bibliography -- Index.

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