Lectures on Lagrangian Torus Fibrations

"This book explains how to use simple 2-dimensional pictures to understand the geometry and topology of 4-dimensional spaces. These spaces are of relevance in Hamiltonian dynamics, in algebraic geometry, and in mathematical string theory. It is suitable for graduate students and researchers in geometry and topology"--

List of contents

1. The Arnold-Liouville theorem; 2. Lagrangian fibrations; 3. Global action-angle coordinates and torus actions; 4. Symplectic reduction; 5. Visible Lagrangian submanifolds; 6. Focus-focus singularities; 7. Examples of focus-focus systems; 8. Almost toric manifolds; 9. Surgery; 10. Elliptic and cusp singularities; A. Symplectic linear algebra; B. Lie derivatives; C. Complex projective spaces; D. Cotangent bundles; E. Moser's argument; F. Toric varieties revisited; G. Visible contact hypersurfaces and Reeb flows; H. Tropical Lagrangian submanifolds; I. Markov triples; J. Open problems; References; Index.

About the author

Jonny Evans is Reader in Pure Mathematics at Lancaster University. He is a geometer, and in 2021 he was awarded an LMS Whitehead Prize for his work on symplectic geometry and singularities.

Product details

• Authors: Jonny Evans, Jonny (University of Lancaster) Evans
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 01.07.2023
• EAN: 9781009372626
• ISBN: 978-1-0-0937262-6
• No. of pages: 243
• Series: London Mathematical Society Student Texts
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; MATHEMATICS / Differential Equations / General, MATHEMATICS / Geometry / General, MATHEMATICS / Topology, geometry, Topology, Differential calculus & equations, Differential calculus and equations