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Surfaces in a background space and the homology of mapping class groups

Surfaces in a background space and the homology of mapping class groups

In this paper we study the topology of the space of Riemann surfaces in a simply connected space X, Sg,n(X,). This is the space consisting of triples, (Fg,n,�,f), where Fg,n is a Riemann surface of genus g and n-boundary components, � is a parameterization of the boundary, @Fg,n, and f …