An introduction to contact topology / / Hansjörg Geiges [[electronic resource]]

• Record Nr.: UNINA9910451146203321
• Autore: Geiges Hansjörg <1966->
• Pubbl/distr/stampa: Cambridge : , : Cambridge University Press, , 2008
• ISBN: 1-107-17883-5; 1-281-24339-6; 9786611243395; 0-511-37796-7; 0-511-37706-1; 0-511-37612-X; 0-511-37461-5; 0-511-61143-9; 0-511-37885-8
• Descrizione fisica: 1 online resource (xv, 440 pages) : digital, PDF file(s)
• Collana: Cambridge studies in advanced mathematics ; ; 109
• Disciplina: 514.72
• Soggetti: Symplectic and contact topology
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and indexes.
• Nota di contenuto: Cover; Half-title; Series-title; Title; Copyright; Dedication; Contents; Contents; Preface; Preface; 1 Facets of contact geometry; 2 Contact manifolds; 3 Knots in contact 3-manifolds; 4 Contact structures on 3-manifolds; 5 Symplectic fillings and convexity; 6 Contact surgery; 7 Further constructions of contact manifolds; 8 Contact structures on 5-manifolds; Appendix A: The generalised Poincaré lemma; Appendix B: Time-dependent vector fields; References; Notation index; Author index; Subject index
• Sommario/riassunto: 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.