2 results
Search Results
Now showing 1 - 2 of 2
Article Liftable Homeomorphisms of Cyclic and Rank Two Finite Abelian Branched Covers Over the Real Projective Plane(Elsevier, 2021) Atalan, Ferihe; Medetogullari, Elif; Ozan, YildirayIn this note, we investigate the property for regular branched finite abelian covers of the real projective plane, where each homeomorphism of the base (preserving the branch locus) lifts to a homeomorphism of the covering surface. (C) 2020 Elsevier B.V. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3Liftable Homeomorphisms of Rank Two Finite Abelian Branched Covers(Springer Basel Ag, 2021) Atalan, Ferihe; Atalan, Ferihe; Medetogullari, Elif; Ozan, Yildiray; Medetoğulları, Elif; Atalan, Ferihe; Medetoğulları, Elif; Mathematics; MathematicsWe 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 Sigma -> S-2 is a regular A-covering branched over n points such that every homeomorphism f:S-2 -> S-2 lifts to Sigma, 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 pi : Sigma -> S-2, where A = ZprxZpt, 1 <= r <= t , all homeomorphisms f:S-2 -> S-2 lift to those of Sigma if and only if t = r or t = r + 1 and p = 3.
