# Symplectic Geometry

@article{Cieliebak1992SymplecticG, title={Symplectic Geometry}, author={Kai Cieliebak}, journal={Acta Applicandae Mathematica}, year={1992}, volume={28}, pages={95-97} }

These are lecture notes for two courses, taught at the University of Toronto in Spring 1998 and in Fall 2000. Our main sources have been the books " Symplectic Techniques " by Guillemin-Sternberg and " Introduction to Symplectic Topology " by McDuff-Salamon, and the paper " Stratified symplectic spaces and reduction " , Ann. of Math. 134 (1991) by Sjamaar-Lerman.

## 857 Citations

NOTES ON SYMPLECTIC TOPOLOGY

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- 2022

These are notes on symplectic topology, based on a graduate course taught at the University of Chicago in Winter 2022

MOMENT MAPS, PSEUDO-HOLOMORPHIC CURVES AND SYMPLECTOMORPHISM GROUPS

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- 2006

These are the notes of a 3-lecture mini-course on some basic topics of symplectic geometry and topology, given at the XIV Fall Workshop on Geometry and Physics, September 14–16, 2005, in Bilbao,…

Harmonic Maps and the Symplectic Category

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- 2014

In the context of the two dimensional sigma model, we show that classical field theory naturally defines a functor from Segal's category of Riemann surfaces to the Guillemin-Sternberg/Weinstein…

Derived Stacks in Symplectic Geometry

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- 2021

This is a survey paper on derived symplectic geometry, that will appear as a chapter contribution to the book "New Spaces for Mathematics and Physics", edited by Mathieu Anel and Gabriel Catren.
Our…

Symplectic and Contact Geometry and Hamiltonian Dynamics

- Mathematics
- 2001

This is an introduction to the contributions by the lecturers at the mini-symposium on symplectic and contact geometry. We present a very general and brief account of the prehistory of the field and…

Symplectic geometry and geometric quantization

- Physics, Mathematics
- 2007

We review in a pedagogical manner the geometrical formulation of classical mechanics in the framework of symplectic geometry and the geometric quantization that associate to a classical system a…

Notes on Lusternik-Schnirelman and Morse Theories

- Mathematics
- 2015

In this chapter (longer than the others) we will present techniques that are close to other modern research themes: existence theorems for critical points of functions. We will move in many…

Remarks on Symplectic Geometry.

- Mathematics
- 2019

We survey the progresses on the study of symplectic geometry past four decades. We briefly deal with the convexity properties of a moment map, the classification of symplectic actions, the symplectic…

SYMPLECTIC GEOMETRY

- Mathematics
- 2001

Symplectic geometry studies the geometry of manifolds equipped with a non-degenerate, closed 2–form. Symplectic structures have their origin in the study of classical mechanics. Important…

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- Mathematics
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This is an extended second edition of "The Topology of Torus Actions on Symplectic Manifolds" published in this series in 1991. The material and references have been updated. Symplectic manifolds and…

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- Mathematics
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The discoveries of the last decades have opened new perspectives for the old field of Hamiltonian systems and led to the creation of a new field: sympletic topology. Surprising rigidity phenomena…

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Note: A basic exposition of classical mechanical systems; 2nd edition Reference CAG-BOOK-2008-008 Record created on 2008-11-21, modified on 2017-09-27