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This textbook offers a concise introduction to symplectic and contact geometry, with a focus on the relationships between these subjects and other topics such as Lie theory and classical mechanics.
Organized into four chapters, this work serves as a stepping stone for readers to delve into the subject, providing a succinct and motivating foundation. The content covers definitions, symplectic linear algebra, symplectic and contact manifolds, Hamiltonian systems, and more. Prerequisite knowledge includes differential geometry, manifolds, algebraic topology, de Rham cohomology, and the basics of Lie groups. Quick reviews are included where necessary, and examples and constructions are provided to foster understanding.
Ideal for advanced undergraduate students and graduate students, this volume can also serve as a valuable resource for independent researchers seeking a quick yet solid understanding of symplectic and contact geometry.
Inhaltsverzeichnis
Preface.- Symplectic linear algebra.- Symplectic manifolds.- Hamiltonian systems.- Contact manifolds.- References.- Index.
Über den Autor / die Autorin
Anahita Eslami Rad is a Researcher at the mathematics department (FaMAF) of the National University of Cordoba, Argentina. She obtained her BSc and MSc in mathematics from the University of Tehran, Iran. Then she moved to Utrecht University, Netherlands, where she studied symplectic geometry and beyond. She received her PhD in mathematics from the Free University of Brussels, Belgium in 2012.
Bericht
"The book comprises four well-organized chapters, each progressively building upon the previous ... . Each chapter is supplemented with examples, exercises, and concise proofs, reflecting the pedagogical origin of the text. The volume ends with a rich bibliography of 56 references. One of the book s notable strengths is its clarity and brevity." (Gabriel Eduard Vilcu, zbMATH 1556.53001, 2025)
This book is called a concise introduction, and many topics are treated quickly. Some subjects are touched on only very briefly (cohomology classes and almost complex structures, for example), and probably deserve more detail and some examples. This is an excellent introduction to the subject for those with sufficient background. It incorporates many topics in relatively few pages, but it is complete, rigorous and thorough. (Bill Satzer, MAA Reviews, November 13, 2024)
