Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Liftable homeomorphisms of rank two finite abelian branched covers
Date
2020
Author
Atalan, Ferihe
Medetoğulları, Elif
Ozan, Yıldıray
Metadata
Show full item record
Item Usage Stats
78
views
0
downloads
Cite This
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
Suggestions
OpenMETU
Core
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...
Liftable homeomorphisms of cyclic and rank two finite abelian branched covers over the real projective plane
Atalan, Ferihe; Medetogullari, Elif; Ozan, Yıldıray (Elsevier BV, 2021-02-01)
© 2020 Elsevier B.V.In 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.
Automorphisms of curve complexes on nonorientable surfaces
Atalan, Ferihe; Korkmaz, Mustafa (2014-01-01)
For a compact connected nonorientable surface N of genus g with n boundary components, we prove that the natural map from the mapping class group of N to the automorphism group of the curve complex of N is an isomorphism provided that g + n >= 5. We also prove that two curve complexes are isomorphic if and only if the underlying surfaces are diffeomorphic.
A note on the generalized Matsumoto relation
DALYAN, ELİF; Medetogullari, Elif; Pamuk, Mehmetcik (2017-01-01)
We give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists.
Legendrian realization in convex Lefschetz fibrations and convex stabilizations
Akbulut, Selman; Arıkan, Mehmet Fırat (Walter de Gruyter GmbH, 2015-05-01)
We show that, up to a Liouville homotopy and a deformation of compact convex Lefschetz fibrations on W, any Lagrangian submanifold with trivial first de Rham cohomology group, embedded on a (symplectic) page of the (induced) convex open book on partial derivative W, can be assumed to be Legendrian in partial derivative W with the induced contact structure. This can be thought as the extension of Giroux's Legendrian realization (which holds for contact open books) for the case of convex open books. We also s...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
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.