An introduction to contact topology

• Verfasst von: Geiges, Hansjörg [VerfasserIn]
• Titel: An introduction to contact topology
• Verf.angabe: Hansjörg Geiges, Universität zu Köln
• Verlagsort: Cambridge ; New York ; Melbourne ; Madrid ; Cape Town ; Singapore ; São Paulo
• Verlag: Cambridge University Press
• E-Jahr: 2008
• Jahr: [2008]
• Umfang: 1 Online-Ressource (xvi, 440 Seiten)
• Illustrationen: Illustrationen
• Gesamttitel/Reihe: Cambridge studies in advanced mathematics ; 109
• Fussnoten: Title from publisher's bibliographic system (viewed on 05 Oct 2015)
• ISBN: 978-0-511-61143-8
• DOI: doi:10.1017/CBO9780511611438
• Schlagwörter: (s)Kontakttopologie / (s)Kontaktmannigfaltigkeit
• Schlagwörter: (s)Kontakttopologie / (s)Kontaktmannigfaltigkeit
• Datenträger: Online-Ressource
• Dokumenttyp: Einführung
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Geiges, Hansjörg, 1966 - : An introduction to contact topology. - 1. publ.. - Cambridge [u.a.] : Cambridge Univ. Press, 2008. - XV, 440 S.
• RVK-Notation: SK 350
• Sach-SW: Harmonic analysis
• Sach-SW: Finite groups
• K10plus-PPN: 883328119
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.