## e-books in Symplectic & Contact Geometry category

**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.

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**3111**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.

(

**3030**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.

(

**4400**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.

(

**5906**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.

(

**6151**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.

(

**6788**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.

(

**7255**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.

(

**8856**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.

(

**9014**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.

(

**7759**views)