Liftable homeomorphisms of rank two finite abelian branched covers

2020
Atalan, Ferihe
Medetoğulları, Elif
Ozan, Yıldıray
We investigate branched regular finite abelian A-covers of the 2-sphere, where every homeomorphism of the base (preserving the branch locus) lifts to a homeomorphism of the covering surface. In this study, we prove that if A is a finite abelian p-group of rank k and Σ → S2 is a regular A-covering branched over n points such that every homeomorphism f : S2 → S2 lifts to Σ, then n = k+1. We will also give a partial classification of such covers for rank two finite p-groups. In particular, we prove that for a regular branched A-covering π : Σ → S2, where A = Zpr × Zpt , 1 ≤ r ≤ t, all homeomorphisms f : S2 → S2 lift to those of Σ if and only if t = r or t = r + 1 and p = 3.
Citation Formats
F. Atalan, E. Medetoğulları, and Y. Ozan, “Liftable homeomorphisms of rank two finite abelian branched covers,” 2020, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/88536.