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Introduction to Symplectic Field Theory

- Y. Eliashberg, A. Givental, H. Hofer
- Mathematics
- 6 October 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… Expand

TOPOLOGICAL CHARACTERIZATION OF STEIN MANIFOLDS OF DIMENSION >2

- Y. Eliashberg
- Mathematics
- 1 March 1990

In this paper I give a completed topological characterization of Stein manifolds of complex dimension >2. Another paper (see [E14]) is devoted to new topogical obstructions for the existence of a… Expand

Classification of overtwisted contact structures on 3-manifolds

- Y. Eliashberg
- Mathematics
- 1 October 1989

A contac t s t ructure on a (2n + l ) -d imensional manifold is a cod imens ion 1 tangent d is t r ibut ion which can be defined (at least locally) by a 1-form 7 with 7/x (d~)" nowhere 0. In this… Expand

Contact 3-manifolds twenty years since J. Martinet's work

- Y. Eliashberg
- Mathematics
- 1992

© Annales de l’institut Fourier, 1992, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions… Expand

Introduction to the h-Principle

- Y. Eliashberg, N. Mishachev
- Mathematics
- 2002

Intrigue Holonomic approximation: Jets and holonomy Thom transversality theorem Holonomic approximation Applications Differential relations and Gromov's $h$-principle: Differential relations Homotopy… Expand

From Stein to Weinstein and Back: Symplectic Geometry of Affine Complex Manifolds

- K. Cieliebak, Y. Eliashberg
- Mathematics
- 27 December 2012

A beautiful and comprehensive introduction to this important field. --Dusa McDuff, Barnard College, Columbia University This excellent book gives a detailed, clear, and wonderfully written treatment… Expand

Few remarks about symplectic filling

- Y. Eliashberg
- Mathematics
- 26 November 2003

We show that any compact symplectic manifold $W,\omega$ with boundary embeds as a domain into a closed symplectic manifold, provided that there exists a contact plane $\xi$ on $\partial W$ which is… Expand

Partially ordered groups and geometry of contact transformations

- Y. Eliashberg, L. Polterovich
- Mathematics
- 13 October 1999

Abstract. We prove that, for a class of contact manifolds, the universal cover of the group of contact diffeomorphisms carries a natural partial order. It leads to a new viewpoint on geometry and… Expand

Effect of Legendrian surgery

- F. Bourgeois, T. Ekholm, Y. Eliashberg
- Mathematics
- 30 October 2009

The paper is a summary of the results of the authors concerning computations of symplectic invariants of Weinstein manifolds and contains some examples and applications. Proofs are sketched. The de… Expand

Geometry of Low-dimensional Manifolds: Filling by holomorphic discs and its applications

- Y. Eliashberg
- Mathematics
- 1991

The survey is devoted to application of the technique of filling by holomorphic discs to different symplectic and complex analytic problems. COMPLEX AND SYMPLECTIC RECOLLECTIONS J -Convexity Let X, J… Expand

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