Please use this identifier to cite or link to this item:
Title: Maps of Archimedean class and operations on dessins
Author: Catalano, Domenico
Breda d'Azevedo, António
Karábas, Ján
Nedela, Roman
Keywords: Action of a group on a surface
Belyı function
Map covering
Issue Date: 23-Mar-2015
Publisher: Elsevier
Abstract: In the present paper we introduce a family of functors (called operations) of the category of hypermaps (dessins) preserving the underlying Riemann surface. The considered family of functors include as particular instances the operations considered by Magot and Zvonkin (2000), Singerman and Syddall (2003), and Girondo (2003). We identify a set of 10 operations in the above infinite family which produce vertex-transitive dessins out of regular ones. This set is complete in the following sense: if a vertex-transitive map arises from a regular dessin H applying an operation, then it can be obtained from a regular dessin on the same surface (possibly different from H) applying one of the 10 operations. The statement includes the classical case when the underlying surface is the sphere.
Peer review: yes
DOI: 10.1016/j.disc.2015.03.001
ISSN: 0012-365X
Appears in Collections:CIDMA - Artigos
AGG - Artigos

Files in This Item:
File Description SizeFormat 
Maps of Archimedean class and operations on dessins.pdfDocumento principal687.37 kBAdobe PDF    Request a copy

FacebookTwitterDeliciousLinkedInDiggGoogle BookmarksMySpace
Formato BibTex MendeleyEndnote Degois 

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.