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Mod $$p$$ homology of the stable mapping class group. (English) Zbl 1074.57013
Let $$F_{g,n}$$ be an oriented surface of genus $$g$$ with $$n$$ boundary components and let $$\Gamma_{g,n}$$ denote the mapping class group of $$F_{g,n}$$, the group of isotopy classes of orientation-preserving diffeomorphisms of $$F_{g,n}$$ fixing each point in a neighborhood of the boundary of $$F_{g,n}$$. In this paper the author calculates the homology groups $$H_*(F_{g,n};{\mathbb{F}}_p)$$ in the stable range. The calculation is based on the proof of Mumford Conjecture given by I. Madsen and M. Weiss.

MSC:
 57M99 General low-dimensional topology 57M50 General geometric structures on low-dimensional manifolds
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