Lifting Homeomorphisms and Cyclic Branched Covers of Spheres
Tyrone Ghaswala, Rebecca R. Winarski
TL;DR
This paper characterizes specific cyclic branched covers of the 2-sphere where all sphere homeomorphisms lift to the cover, addressing a question from Birman and Hilden's earlier work.
Contribution
It provides a complete characterization of cyclic branched covers of the sphere with the lifting property for all homeomorphisms.
Findings
Identifies conditions under which sphere homeomorphisms lift to the cover.
Answers a previously open question from Birman and Hilden.
Advances understanding of symmetries in branched covers.
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].
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