Breda d’Azevedo, Antonio J.; Jones, Gareth A. Double coverings and reflexive abelian hypermaps. (English) Zbl 0967.05027 Beitr. Algebra Geom. 41, No. 2, 371-389 (2000). Summary: We describe a general theory of hypermaps on surfaces, possibly non-orientable or with boundary. This includes techniques for constructing hypermaps as products and as double coverings, and for representing hypermaps as maps using homomorphisms between extended triangle groups. As a corollary we obtain a classification of the 16 reflexible hypermaps with abelian automorphism groups. Cited in 8 Documents MSC: 05C10 Planar graphs; geometric and topological aspects of graph theory 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 57M15 Relations of low-dimensional topology with graph theory Keywords:hypermaps on surfaces; double coverings; triangle groups; reflexible hypermaps; abelian automorphism groups PDFBibTeX XMLCite \textit{A. J. Breda d'Azevedo} and \textit{G. A. Jones}, Beitr. Algebra Geom. 41, No. 2, 371--389 (2000; Zbl 0967.05027) Full Text: EuDML EMIS