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 Ana Cannas da Silva - Princeton University
An overview of symplectic geometry – the geometry of symplectic manifolds. From a language of classical mechanics, symplectic geometry became a central branch of differential geometry and topology. This survey gives a partial flavor on this field.
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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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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.