Lectures on Lagrangian Torus Fibrations

ISBN-13: 9781009372633 / Miękka / 2023 / 243 str.

Jonny (University of Lancaster) Evans

Opis

Comprehensive and visual introduction to the geometry of 4-dimensional symplectic manifolds via 2-dimensional almost-toric diagrams.

Recenzje

'This is a lucid and engaging introduction to the fascinating world of (almost) toric geometry, in which one can understand the properties of Lagrangian and symplectic submanifolds in four dimensions simply by drawing suitable two-dimensional diagrams. The book has many illustrations and intricate examples.' Dusa McDuff, Barnard College, Columbia University

Spis treści

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.