This book presents the first steps of a theory of confoliations designed to link geometry and topology of three-dimensional contact structures with the geometry and topology of codimension-one foliations on three-dimensional manifolds. Developing almost independently, these theories at first glance belonged to two different worlds: The theory of foliations is part of topology and dynamical systems, while contact geometry is the odd-dimensional ''brother'' of symplectic geometry. However, both theories have developed a number of striking similarities. Confoliationswhich interpolate between contact structures and codimension-one foliationsshould help us to understand better links between the two theories. These links provide tools for transporting results from one field to the other. Features: A unified approach to the topology of codimension-one foliations and contact geometry. Insight on the geometric nature of integrability. New results, in particular on the perturbation of confoliations into contact structures.
This book presents the first steps of a theory of confoliations designed to link geometry and topology of three-dimensional contact structures with the geometry and topology of codimension-one foliations on three-dimensional manifolds. Developing almost independently, these theories at first glance belonged to two different worlds: The theory of foliations is part of topology and dynamical systems, while contact geometry is the odd-dimensional ''brother'' of symplectic geometry. However, both theories have developed a number of striking similarities. Confoliationswhich interpolate between contact structures and codimension-one foliationsshould help us to understand better links between the two theories. These links provide tools for transporting results from one field to the other. Features: A unified approach to the topology of codimension-one foliations and contact geometry. Insight on the geometric nature of integrability. New results, in particular on the perturbation of confoliations into contact structures.
Product Details
ISBN-13: | 9780821807767 |
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Publisher: | American Mathematical Society |
Publication date: | 11/26/1997 |
Series: | University Lecture Series , #13 |
Pages: | 66 |
Product dimensions: | 9.70(w) x 6.80(h) x 0.20(d) |