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Flow Lines and Algebraic Invariants in Contact Form Geometry

  • Abbas Bahri

Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 53)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Introduction, Statement of Results, and Discussion of Related Hypotheses

  3. Outline of the Book

    1. Abbas Bahri
      Pages 15-16
  4. Review of the Previous Results, Some Open Questions

    1. Front Matter
      Pages 17-17
    2. Abbas Bahri
      Pages 19-35
  5. Intermediate Section: Recalling the Results Described in the Introduction, Outlining the Content of the Next Sections and How These Results are Derived

  6. Technical Study of the Critical Points at Infinity: Variational Theory without the Fredholm Hypothesis

    1. Front Matter
      Pages 75-75
    2. Abbas Bahri
      Pages 77-102
  7. Removal of (A5)

  8. Conditions (A2)-(A3)-(A4)-(A6)

    1. Front Matter
      Pages 195-195
    2. Abbas Bahri
      Pages 197-205
    3. Abbas Bahri
      Pages 207-211
    4. Abbas Bahri
      Pages 213-214
    5. Abbas Bahri
      Pages 215-216
  9. Back Matter
    Pages 217-225

About this book

Introduction

This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology).  In particular, this work develops a novel algebraic tool in this field: rooted in the concept of critical points at infinity, the new algebraic invariants defined here are useful in the investigation of contact structures and Reeb vector fields.

The book opens with a review of prior results and then proceeds through an examination of variational problems, non-Fredholm behavior, true and false critical points at infinity, and topological implications.  An increasing convergence with regular and singular Yamabe-type problems is discussed, and the intersection between contact form and Riemannian geometry is emphasized, with a specific focus on a unified approach to non-compactness in both disciplines.  Fully detailed, explicit proofs and a number of suggestions for further research are provided throughout.

Rich in open problems and written with a global view of several branches of mathematics, this text lays the foundation for new avenues of study in contact form geometry.  Graduate students and researchers in geometry, partial differential equations, and related fields will benefit from the book's breadth and unique perspective.

Keywords

Algebra ODEs PDEs Riemannian geometry algebraic invariant algebraic topology differential geometry homology nonlinear analysis partial differential equation

Authors and affiliations

  • Abbas Bahri
    • 1
  1. 1.Department of MathematicsRutgers UniversityNew BrunswickUSA

Bibliographic information