Regular Maps on a Given Surface: A Survey

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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.