Künneth Geometry: Symplectic Manifolds and their Lagrangian Foliations

M. J. D. Hamilton; D. Kotschick

doi:10.1017/9781108902977

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.

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Künneth Geometry

Symplectic Manifolds and their Lagrangian Foliations

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

1 - Introduction
pp 1-12

2 - Linear Algebra and Bundle Theory
pp 13-29

3 - Symplectic Geometry
pp 30-41

4 - Foliations and Connections
pp 42-56

5 - Künneth Structures
pp 57-72

6 - The Künneth Connection
pp 73-84

7 - The Curvature of a Künneth Structure
pp 85-106

8 - Hypersymplectic Geometry
pp 107-122

9 - Nilmanifolds
pp 123-150

10 - Four-manifolds
pp 151-178

Bibliography
pp 179-184

Index
pp 185-192

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Künneth Geometry

Symplectic Manifolds and their Lagrangian Foliations

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