A primer on mapping class groups

@inproceedings{Farb2013APO,
  title={A primer on mapping class groups},
  author={Benson Farb and Danielle N Margalit},
  year={2013}
}
Given a compact connected orientable surface S there are two fundamental objects attached: a group and a space. The group is the mapping class group of S, denoted by Mod(S). This group is defined by the isotopy classes of orientation-preserving homeomorphism from S to itself. Equivalently, Mod(S) may be defined using diffeomorphisms instead of homeomorphisms or homotopy classes instead of isotopy classes. The space is the Teichmüller space of S, Teich(S). Teichmüller space and moduli space are… 
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References

Mappings (Mathematics) 2. Class groups
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