Künneth Geometry

Symplectic Manifolds and their Lagrangian Foliations

AvM. J. D. Hamilton,D. Kotschick

Inbunden, Engelska, 2023

Del 108 i serien London Mathematical Society Student Texts

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Beskrivning

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.

Produktinformation

Utgivningsdatum:2023-12-21
Mått:155 x 235 x 15 mm
Vikt:421 g
Format:Inbunden
Språk:Engelska
Serie:London Mathematical Society Student Texts
Antal sidor:200
Förlag:Cambridge University Press
ISBN:9781108830713

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Mer om författaren

M.J.D. Hamilton has been teaching mathematics at all levels at Ludwig-Maximilians-Universität München and Universität Stuttgart for the past fifteen years. He is interested in the interactions of geometry and theoretical physics, and is known for his successful transfer of ideas between the two subjects. He is the author of the acclaimed textbook 'Mathematical Gauge Theory' (2017). D. Kotschick has been Professor of Mathematics, holding the Chair of Differential Geometry, at Ludwig-Maximilians-Universität München for twenty-five years. A researcher of exceptionally broad knowledge and interests, he is an internationally recognised expert in several areas of geometry and topology. He is known for the depth and insight of his research as well as for his meticulous scholarship and the clarity of his writing. He is a long-standing member of the London Mathematical Society and in 1996 received the Lucien Godeaux Prize of the Royal Society of Liège.

Innehållsförteckning

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.