The Symplectic Symmetry Group of 4-Manifolds

Friday, 24 March 2017 - 3:30pm
Tian-Jun Li, Univ. of Minnesota
LD 229

A symplectic manifold is a smooth manifold equipped with a symplectic form,

which is a closed and non-degenerate 2-form, and a symmetry of a  symplectic manifold is a diffeomorphism preserving the symplectic form. The   symmetry group Symp(M) of a symplectic manifold M   is  an  infinite dimensional Lie group.  This talk is on some recent advances about the  topology of Symp(M) for 4-dimensional symplectic manifolds, especially rational surfaces. The rich topology structure  is detected by the action of Symp(M) on

various geometric objects associated to M, the homology, the space of almost complex structures and the space of immersed symplectic spheres. 

An interesting aspect is the appearance of Dykin diagram. 

This  is a joint work with Jun Li and Weiwei Wu.