Symplectic & Contact Geometry

e-books in Symplectic & Contact Geometry category

Symplectic, Poisson, and Noncommutative Geometry
by Tohru Eguchi, et al. - Cambridge University Press , 2014
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 ...
(5192 views)

Lecture Notes on Embedded Contact Homology
by Michael Hutchings - arXiv , 2013
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.
(8025 views)

Introduction to the Basics of Heegaard Floer Homology
by Bijan Sahamie - arXiv , 2010
This is an introduction to the basics of Heegaard Floer homology with some emphasis on the hat theory and to the contact geometric invariants in the theory. It is designed to be comprehensible to people without any prior knowledge of the subject.
(8096 views)

Symplectic Geometry of Quantum Noise
by Leonid Polterovich - arXiv , 2012
We discuss a quantum counterpart of certain constraints on Poisson brackets coming from 'hard' symplectic geometry. They can be interpreted in terms of the quantum noise of observables and their joint measurements in operational quantum mechanics.
(9964 views)

First Steps Towards a Symplectic Dynamics
by Barney Bramham, Helmut Hofer - arXiv , 2011
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.
(11978 views)

Contact Geometry
by Hansjoerg Geiges - arXiv , 2004
This is an introductory text on the more topological aspects of contact geometry. After discussing some of the fundamental results of contact topology, I move on to a detailed exposition of the original proof of the Lutz-Martinet theorem.
(12136 views)

Lectures on Holomorphic Curves in Symplectic and Contact Geometry
by Chris Wendl - arXiv , 2010
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.
(11832 views)

Introduction to Symplectic Field Theory
by Y. Eliashberg, A. Givental, H. Hofer - arXiv , 2000
We sketch in this article a new theory, which we call Symplectic Field Theory or SFT, which provides an approach to Gromov-Witten invariants of symplectic manifolds and their Lagrangian submanifolds in the spirit of topological field theory.
(13278 views)

Introduction to Symplectic and Hamiltonian Geometry
by Ana Cannas da Silva , 2007
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.
(15091 views)

Lectures on Symplectic Geometry
by Ana Cannas da Silva - Springer , 2006
An introduction to symplectic geometry and topology, it provides a useful and effective synopsis of the basics of symplectic geometry and serves as the springboard for a prospective researcher. The text is written in a clear, easy-to-follow style.
(15532 views)

Symplectic Geometry
by Ana Cannas da Silva - Princeton University , 2004
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.
(13291 views)