Regular Maps on a Given Surface: A Survey

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Abstract

Regular maps are cellular decompositions of closed surfaces with the highest ‘level of symmetry’, meaning that the automorphism group of the map acts regularly on flags. We survey the state-of-the-art of the problem of classification of regular maps on a given surface and outline directions of future research in this area.

This research was sponsored in part by the U.S.-Slovak Science and Technology Joint Fund, Project Number 020/2001. Partial support from the RSNZ Marsden Fund is also gratefully acknowledged.