Künneth Geometry
Symplectic Manifolds and their Lagrangian Foliations

An elegant introduction to symplectic geometry and Lagrangian foliations, including a systematic study of bi-Lagrangian geometry.

M. J. D. Hamilton (Author), D. Kotschick (Author)

9781108830713, Cambridge University Press

Hardback, published 21 December 2023

200 pages
23.5 x 15.5 x 1.5 cm, 0.421 kg

This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses Künneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.

1. Introduction
2. Linear algebra and bundle theory
3. Symplectic geometry
4. Foliations and connections
5. Künneth structures
6. The Künneth connection
7. The curvature of a Künneth structure
8. Hypersymplectic geometry
9. Nilmanifolds
10. Four-manifolds.

Subject Areas: Geometry [PBM]