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Liftable homeomorphisms of rank two finite abelian branched covers
Date
2020
Author
Atalan, Ferihe
Medetoğulları, Elif
Ozan, Yıldıray
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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.
Subject Keywords
Branched Covers
,
Mapping Class Group
,
Automorphisms Of Groups
URI
https://hdl.handle.net/11511/88536
Journal
Archiv der Mathematik
DOI
https://doi.org/https://doi.org/10.1007/s00013-020-01501-z
Collections
Department of Mathematics, Article
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Liftable homeomorphisms of rank two finite abelian branched covers
Atalan, Ferihe; Medetogullari, Elif; Ozan, Yıldıray (2020-11-01)
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 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 prov...
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F. Atalan, E. Medetoğulları, and Y. Ozan, “Liftable homeomorphisms of rank two finite abelian branched covers,”
Archiv der Mathematik
, 2020, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/88536.