| Résume | Abstract : In the moduli space of marked curves, we consider the locus of curves carrying a holomorphic differential with prescribed orders at the markings. When these orders are even, this locus has two connected component determined by the sign of a canonical spin structure. I will explain how to compute the class of the cycle defined by each connected component. On the hand, I will highlight some of the difficulties compared to the computation of the class of the union of the two components (solved around 2017), and on another hand, I will and explain the relevance of this problem from the perspective of Witten’s classes (joint work D. Holmes and G. Politopoulos).
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