Mod 2 homology of the stable spin mapping class group

@article{Galatius2005Mod2H,
  title={Mod 2 homology of the stable spin mapping class group},
  author={S{\o}ren Galatius},
  journal={Mathematische Annalen},
  year={2005},
  volume={334},
  pages={439-455}
}
Using the main result of Madsen and Weiss [MW], we compute the mod 2 homology of spin mapping class groups in the stable range. In earlier work [G] we computed the stable mod p homology of the oriented mapping class group, and the methods and results here are very similar. The forgetful map from the spin mapping class group to the oriented mapping class groups induces a homology isomorphism for odd p but for p=2 it is far from being an isomorphism. We include a general discussion of tangential… CONTINUE READING

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