Departamento de Matematica, Universidade de Aveiro, 3800 Aveiro, Portugal; Department of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom
Abstract: 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.
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