Symplectic Geometry

  title={Symplectic Geometry},
  author={Kai Cieliebak},
  journal={Acta Applicandae Mathematica},
  • K. Cieliebak
  • Published 1992
  • Mathematics
  • Acta Applicandae Mathematica
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. 
These are notes on symplectic topology, based on a graduate course taught at the University of Chicago in Winter 2022
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
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
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
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
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
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.
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 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


Lectures on Symplectic Manifolds
Introduction Symplectic manifolds and lagrangian submanifolds, examples Lagrangian splittings, real and complex polarizations, Kahler manifolds Reduction, the calculus of canonical relations,
The Topology of Torus Actions on Symplectic Manifolds
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
Symplectic Invariants and Hamiltonian Dynamics
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
Moment Maps and Combinatorial Invariants of Hamiltonian Tn-spaces
Basic definitions and examples the Duistermaat-Heckman theorem multiplicities as invariants of reduced spaces partition functions. Appendix I: Toric varieties. Appendix 2: Kaehler structures on toric
Some simple examples of symplectic manifolds
This is a construction of closed symplectic manifolds with no Kaehler structure. A symplectic manifold is a manifold of dimension 2k with a closed 2-form a such that ak is nonsingular. If M2k is a
Pseudo holomorphic curves in symplectic manifolds
Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called
The analogue of Theorem A for the topological case was proved by H. Kneser [2]. The problem in his case seems to be of a different nature from the differentiable case. J. Munkres [3] has proved that
The local structure of Poisson manifolds
Varietes de Poisson et applications. Decomposition. Structures de Poisson lineaires. Approximation lineaire. Systemes hamiltoniens. Le probleme de linearisation. Groupes de fonction, realisations et
Mathematical Methods of Classical Mechanics
Part 1 Newtonian mechanics: experimental facts investigation of the equations of motion. Part 2 Lagrangian mechanics: variational principles Lagrangian mechanics on manifolds oscillations rigid
Introduction to mechanics and symmetry
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