  This is the final version of my master thesis. I prove that there are no
twist star products on the 2-sphere and on the higher genus pretzel surfaces
deforming a symplectic structure. One of the key arguments is that a connected
compact symplectic manifold endowed with a twist star product has to be a
homogeneous space. Furthermore, there is a non-degenerate r-matrix on a Lie
algebra whose Lie group is acting transitively and effectively on the manifold
in this case. I recap the theory of homogeneous spaces, in particular the
classification of transitive effective actions on the 2-sphere, and discuss the
notion of r-matrices and Drinfel'd twists. Some results of this thesis are
available as a preprint with Pierre Bieliavsky, Chiara Esposito and Stefan
Waldmann on arxiv.org under the title "Obstructions for Twist Star Products".
