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4 results

  • 1 - Introduction

  • M. J. D. Hamilton, Universität Stuttgart, D. Kotschick, Ludwig-Maximilians-Universität München
  • Book:
    Künneth Geometry
    Published online:
    07 December 2023
    Print publication:
    21 December 2023, pp 1-12

  • Summary

    This book is about the geometry and topology of symplectic manifolds equipped with pairs of complementary Lagrangian foliations. The resulting structure is very rich, intertwining symplectic geometry, the theory of foliations, dynamical systems, and pseudo-Riemannian geometry in interesting ways.

    Before describing the contents of the book in detail, we want to discuss a few motivating vignettes. The first two of these are to be kept in mind as motivational background, whereas the third and fourth ones will be taken up again and again later in the book.

  • 5 - Künneth Structures

  • M. J. D. Hamilton, Universität Stuttgart, D. Kotschick, Ludwig-Maximilians-Universität München
  • Book:
    Künneth Geometry
    Published online:
    07 December 2023
    Print publication:
    21 December 2023, pp 57-72

  • Summary

    With this chapter we begin the main part of our discussion of Künneth geometry. We first define Künneth and almost Künneth structures. The former are the main structures whose geometry we investigate in this and the coming chapters. In this chapter we give only their most basic properties, and we discuss their automorphism groups. Most of this chapter consists of the discussion of several classes of examples.

Künneth Geometry
  • Symplectic Manifolds and their Lagrangian Foliations
  • M. J. D. Hamilton, D. Kotschick
  • Published online:
    07 December 2023
    Print publication:
    21 December 2023
  • 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.