Connected components of the moduli spaces of Abelian differentials with prescribed singularities

@article{Kontsevich2002ConnectedCO,
  title={Connected components of the moduli spaces of Abelian differentials with prescribed singularities},
  author={Maxim Kontsevich and Anton Zorich},
  journal={Inventiones mathematicae},
  year={2002},
  volume={153},
  pages={631-678}
}
Consider the moduli space of pairs (C,ω) where C is a smooth compact complex curve of a given genus and ω is a holomorphic 1-form on C with a given list of multiplicities of zeroes. We describe connected components of this space. This classification is important in the study of dynamics of interval exchange transformations and billiards in rational polygons, and in the study of geometry of translation surfaces. 
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