This clear and elegant text introduces Kuenneth, 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 Kuenneth 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.
Reihe
Sprache
Verlagsort
Produkt-Hinweis
Illustrationen
Worked examples or Exercises
Maße
Höhe: 152 mm
Breite: 228 mm
Dicke: 16 mm
Gewicht
ISBN-13
978-1-108-82875-8 (9781108828758)
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Schweitzer Klassifikation
M.J.D. Hamilton has been teaching mathematics at all levels at Ludwig-Maximilians-Universitaet Muenchen and Universitaet 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-Universitaet Muenchen 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 Liege.
Autor*in
Universitaet Stuttgart
Ludwig-Maximilians-Universitaet Muenchen
1. Introduction; 2. Linear algebra and bundle theory; 3. Symplectic geometry; 4. Foliations and connections; 5. Kuenneth structures; 6. The Kuenneth connection; 7. The curvature of a Kuenneth structure; 8. Hypersymplectic geometry; 9. Nilmanifolds; 10. Four-manifolds.
