African Diaspora Journal of Mathematics

Introduction to the Group of Symplectomorphisms

Augustin Banyaga

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Abstract

In these Lecture Notes of a mini-course delivered in the " Séminaire Itinérant de Géometrie et Physique Mathématique, " Geometry and Physics V" at the University Cheikh Anta Diop, Dakar in May 2007, we introduce the group of symplectic diffeomorphisms, the main results on its algebraic structure and on some of its local and global properties. This survey culminates with the most recent results on Hofer geometry, the definitions of the groups of symplectic and hamiltonian homeomorphisms, and the introduction to the $C^0$ symplectic topology.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 9, Number 2 (2009), 120-138.

Dates
First available in Project Euclid: 31 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1270067494

Mathematical Reviews number (MathSciNet)
MR2575307

Zentralblatt MATH identifier
1268.57012

Subjects
Primary: 55D05
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]

Keywords
$C^0$ symplectic topology Hofer geometry Hofer topology hamiltonian topology symplectomorphism hamiltonian diffeomorphisms Arnold conjecture Floer homology symplectic rigidity symplectic capacity symplectic homeomorphisms Hamiltonian homeomorphism

Citation

Banyaga, Augustin. Introduction to the Group of Symplectomorphisms. Afr. Diaspora J. Math. (N.S.) 9 (2009), no. 2, 120--138. https://projecteuclid.org/euclid.adjm/1270067494


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