Lifting Homeomorphisms and Cyclic Branched Covers of Spheres
  We characterize the cyclic branched covers of the 2-sphere where every homeomorphism of the sphere lifts to a homeomorphism of the covering surface. This answers a question that appeared in an early version of the erratum of Birman and Hilden [2]. 
Tyrone Ghaswala and Rebecca R. Winarski
math.GT