The singular simplicial complex S •(X) of a topological space X is the nerve of X with respect to the standard cosimplicial topological space Δ Top:Δ→Top:
S_n(X) = Hom_{Top}(\Delta_{Top}^n, X) \,.
This is always a Kan complex and as such has the interpretation of the fundamental ∞-groupoid Π(X) of X.