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O symetrii

Kędra Jarek

Wiadomości Matematyczne

2008

T. 44, Nr 1

23--33

The present paper is a survey on the topology of diffeomomorphism groups of smooth manifolds. We start with a very mild introduction of the concept of symmetry. We show that symmetries of a space form a topological group. We present some classical results about the topology of diffeomorphism groups of surfaces and four dimensional symplectic manifolds. Then we survey on author’s results about the topology of symplectic diffeomorphisms, Hamiltonian actions of compact Lie groups and characteristic classes.