Representing Dehn Twists with Branched Coverings

We show that any homologically nontrivial Dehn twist of a compactsurface F with boundary is the lifting of a half-twist in thebraid group , with respectto a suitable branched covering p : F B². In particular, weallow the surface to have disconnected boundary. As a consequence,any allowable Lefschetz fibration on B² is a branched coveringof B² x B².