Symplectic, Poisson, and Noncommutative Geometry
by Tohru Eguchi, et al.
Publisher: Cambridge University Press 2014
Number of pages: 290
Symplectic geometry has its origin in physics, but has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics; for example, Floer theory has contributed new insights to quantum field theory.
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by Barney Bramham, Helmut Hofer - arXiv
Both dynamical systems and symplectic geometry have rich theories and the time seems ripe to develop the common core with integrated ideas from both fields. We discuss problems which show how dynamical systems and symplectic ideas come together.
by Chris Wendl - arXiv
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves. From the table of contents: Introduction; Local properties; Fredholm theory; Moduli spaces; Bubbling and nonsqueezing.
by Michael Hutchings - arXiv
These notes give an introduction to embedded contact homology (ECH) of contact three-manifolds, gathering many basic notions which are scattered across a number of papers. We also discuss the origins of ECH, including various remarks and examples.
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The text covers foundations of symplectic geometry in a modern language. It describes symplectic manifolds and their transformations, and explains connections to topology and other geometries. It also covers hamiltonian fields and hamiltonian actions.