Title: Stable Homology of Aut(F_n)

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Abstract: Let Aut(F_n) denote the automorphism group of a free group on n generators. It is known that H_k(Aut(F_n)) is independent of n as long as n >> k. There is a natural homomorphism from the symmetric group S_n to Aut(F_n), I will sketch a proof that it induces an isomorphism from H_k(S_n) to H_k(Aut(F_n)) for n >> k. An important point of view here is that the classifying space BAut(F_n) can be thought of as a moduli space of metric graphs, i.e. graphs equipped with metrics, considered up to isometry.