Representing Dehn Twists with Branched Coverings

Abstract

We show that any homologically non-trivial Dehn twist of a compact surface F with boundary is the lifting of a half-twist in the braid group Bn, with respect to a suitable branched covering p : F → B. In particular, we allow the surface to have disconnected boundary. As a consequence, any allowable Lefschetz fibration on B is a branched covering of B × B. 

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