Teleman's classification of 2D semisimple cohomological field theories

In his 2011 paper, Teleman proved that a cohomological field theory on the moduli space ${\bar{\mathcal{M}}}_{g,n}$ of stable complex curves is uniquely determined by its restriction to the smooth part ${\mathcal{M}}_{g,n}$, provided that the underlying Frobenius algebra is semisimple. This leads to a classification of all semisimple cohomological field theories. The present paper, the outcome of the author’s master’s thesis, presents Teleman’s proof following his original paper. The author claims no originality: the main motivation has been to keep the exposition as complete and self-contained as possible.