Bi-rotary Maps of Negative Prime Characteristic

Breda d’Azevedo, Antonio; Catalano, Domenico A. and Širáň, Jozef (2019). Bi-rotary Maps of Negative Prime Characteristic. Annals of Combinatorics, 23(1) pp. 27–50.

DOI: https://doi.org/10.1007/s00026-019-00421-2

Abstract

Bi-orientable maps (also called pseudo-orientable maps) were introduced by Wilson in the seventies to describe non-orientable maps with the property that opposite orientations can consistently be assigned to adjacent vertices. In contrast to orientability, which is both a combinatorial and topological property, bi-orientability is only a combinatorial property. In this paper we classify the bi-orientable maps whose local-orientation-preserving automorphism groups act regularly on arcs, called here bi-rotary maps, of negative prime Euler characteristic. Unlike other classification results for highly symmetric maps on such surfaces we do not use the Gorenstein-Walter result on the structure of groups with dihedral Sylow 2-subgroups.

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