Existence of Engel structures [Elektronische Ressource] / vorgelegt von Thomas Vogel

Existence of Engel structuresThomas VogelExistence of Engel structuresDissertation zur Erlangung des Doktorgradesan der Fakultat¨ fur¨ Mathematik, Informatik und Statistikder Ludwig–Maximilians–Universitat¨ Munchen¨Vorgelegt am 17. Marz¨ 2004 vonThomas VogelErstgutachter Prof. Dieter Kotschick, D. Phil.Zweitgutachter Prof. Dr. Kai Cieliebak¨auswartige Gutachter Prof. Dr. Yakov Eliashberg (Stanford University, USA)Prof. Dr. Michele` Audin (Universite´ Louis Pasteur, Strasbourg, France)Tag der mundlichen¨ Prufung¨ 13. Juli 2004ContentsChapter 1. Introduction 31.1. Contact topology 41.2. First results on Engel structures 61.3. Constructions of Engel manifolds 7Chapter 2. Contact topology 132.1. Basic results on contact structures 142.2. Legendrian curves 182.3. Facts from the theory of convex surfaces 242.4. Bypasses in overtwisted contact structures 27Chapter 3. First results on Engel structures 333.1. Even contact structures 343.2. Engel structures – Definition and first examples 373.3. Topology of Engel manifolds 493.4. Deformations of Engel structures 513.5. Engel vector fields 573.6. Analogues of Gray’s theorem 61Chapter 4. Round handles 674.1. Generalities 684.2. Model Engel structures on round handles 764.3. Relations between the models onR andR 831 2Chapter 5. Closed Engel manifolds from round handles 935.1. Gluing Engel structures 945.2. Vertical modifications of transversal boundaries 965.3. Doubles 995.4.