Symplectic and Contact Geometry
A Concise Introduction
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Beschreibung
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.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.Offers a succinct introduction to the topic, focusing on its relationship with Lie theory and classical mechanics Covers symplectic linear algebra, Hamiltonian systems, Darboux' theorem, and Legendrian submanifolds, and more Provides a motivating foundation for students and independent researchers
Autor*in
Anahita Eslami Rad
Themen in »Symplectic and Contact Geometry«
symplectic manifold symplectic form Hermitian form Lagrangian submanifold symplectomorphism almost complex structure Hamiltonian system classical mechanics Poisson bracket Hamiltonian group action
Stimmen zu »Symplectic and Contact Geometry«
"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)
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