  In genus two and higher, the fundamental group of a closed surface acts
naturally on the curve complex of the surface with one puncture. Combining
ideas from previous work of Kent--Leininger--Schleimer and Mitra, we construct
a universal Cannon--Thurston map from a subset of the circle at infinity for
the closed surface group onto the boundary of the curve complex of the
once-punctured surface. Using the techniques we have developed, we also show
that the boundary of this curve complex is locally path-connected.
