Lifting Homeomorphisms and Cyclic Branched Covers of Spheres

Abstract

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].

5 pages, 1 figure. Minor changes from version 1 to take into account referee's comments

Cited by in corpus (6)

• The Birman-Hilden theory
• Mapping class groups of covers with boundary and braid group embeddings
• Generating the liftable mapping class groups of regular cyclic covers
• A small generating set for the balanced superelliptic handlebody group
• Lifting homeomorphisms and finite abelian branched covers of the 2-sphere
• Generating the liftable mapping class groups of cyclic covers of spheres