Jonny Evans (University of Lancaster)

Lectures on Lagrangian Torus Fibrations

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• London Mathematical Society Student Texts
• Verlag: Cambridge University Press
• Seitenzahl: 243
• Erscheinungstermin: 20. Juli 2023
• Englisch
• Abmessung: 229mm x 152mm x 14mm
• Gewicht: 370g
• ISBN-13: 9781009372633
• ISBN-10: 1009372637
• Artikelnr.: 67793572

Autorenporträt

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.

Inhaltsangabe

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.