Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and ...
Read More
Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kahler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.
Read Less
Add this copy of An Introduction to Symplectic Geometry (Graduate to cart. $71.32, Sold by Zubal Books rated 4.0 out of 5 stars, ships from Cleveland, OH, UNITED STATES, published 2000 by American Mathematical Society.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
195 pp., hardcover, new. -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
Add this copy of An Introduction to Symplectic Geometry (Graduate to cart. $116.99, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2000 by American Mathematical Society.
Add this copy of An Introduction to Symplectic Geometry to cart. $149.83, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2011 by American Mathematical Society.
Add this copy of An Introduction to Symplectic Geometry (Graduate to cart. $154.71, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2000 by American Mathematical Society.
Add this copy of An Introduction to Symplectic Geometry to cart. $160.06, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2001 by American Mathematical Society.
Add this copy of An Introduction to Symplectic Geometry: 26 (Graduate to cart. $180.00, new condition, Sold by Kennys.ie rated 4.0 out of 5 stars, ships from Galway, IRELAND, published 2011 by American Mathematical Society.
Add this copy of An Introduction to Symplectic Geometry (Graduate to cart. $180.66, new condition, Sold by Just one more Chapter rated 3.0 out of 5 stars, ships from Miramar, FL, UNITED STATES, published 2000 by American Mathematical Society.
Add this copy of An Introduction to Symplectic Geometry (Graduate to cart. $188.67, new condition, Sold by Kennys.ie rated 4.0 out of 5 stars, ships from Galway, IRELAND, published 2001 by American Mathematical Society.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
New. Symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book presents an introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. Series: Graduate Studies in Mathematics. Num Pages: 224 pages, Illustrations. BIC Classification: PBMP. Category: (P) Professional & Vocational. Dimension: 265 x 186 x 14. Weight in Grams: 546. 2000. Hardcover.....We ship daily from our Bookshop.
