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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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