Foliations on surfaces / Igor Nikolaev
Type de document : Livre numériqueCollection : Ergebnisse der mathematik und ihrer grenzgebiete, 41Langue : anglais.Éditeur : Berlin : Springer, cop. 2001ISBN: 9783540675242.ISSN: 0071-1136.Sujet MSC : 57R30, Manifolds and cell complexes, Foliations in differential topology; geometric theory37C85, Smooth dynamical systems: general theory, Dynamics induced by group actions other than ℤ and ℝ, and ℂ
37D15, Dynamical systems with hyperbolic behavior, Morse-Smale systems
53C12, Global differential geometry, Foliations (differential geometric aspects)
57M50, Manifolds and cell complexes - General low-dimensional topology, General geometric structures on low-dimensional manifoldsEn-ligne : Springerlink | MSN | Zentralblatt
In this book, the author studies foliations on surfaces from various points of view. The book is divided into two parts, the first part dealing with the basic theory of foliations, and the second part dealing with applications. One has to note first that, by an Euler characteristic argument, the only surfaces which carry foliations are the torus and the Klein bottle. But there are singular foliations on every surface, and in fact there is a vast theory of foliations on surfaces. For instance, a foliation defined by a vector field has singular points at the zeroes of this vector field. The author considers here more general singular points of foliations, with the restriction that these points are isolated points on the surface. ... (MSN)
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