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Confoliations
Yakov M. Eliashberg, Stanford University, CA, and William P. Thurston, University of California, Davis, CA
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University Lecture Series
1998; 66 pp; softcover
Volume: 13
ISBN-10: 0-8218-0776-5
ISBN-13: 978-0-8218-0776-7
List Price: US$20
Member Price: US$16
Order Code: ULECT/13
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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. Confoliations--which interpolate between contact structures and codimension-one foliations--should 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.

Readership

Graduate students and research mathematicians working in differential and symplectic geometry, low-dimensional topology, the theory of foliations and several complex variables; some physicists and engineers.

Reviews

"Go out and buy this book ..."

-- Bulletin of the London Mathematical Society

"As this monograph shows and, one can expect future research will confirm, this unifying approach to the hitherto seemingly independent theories of foliations and contact structures is extremely fruitful ... a veritable cornucopia of ideas and surprising links between contact geometry and the theory of foliations."

-- Mathematical Reviews

Table of Contents

  • Geometric nature of integrability
  • Perturbation of confoliations into contact structures
  • Taut vs. tight
  • Bibliography
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