Map operations and k-orbit maps |
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| Authors: | Alen Orbani? Daniel Pellicer |
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| Affiliation: | a University of Ljubljana, Faculty of Mathematics and Physics, Jadranska 21, 1000 Ljubljana, Slovenia
b York University, Department of Mathematics and Statistics, Toronto, Ontario, Canada, M3J 1P3 |
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| Abstract: | A k-orbit map is a map with k flag-orbits under the action of its automorphism group. We give a basic theory of k-orbit maps and classify them up to k?4. “Hurwitz-like” upper bounds for the cardinality of the automorphism groups of 2-orbit and 3-orbit maps on surfaces are given. Furthermore, we consider effects of operations like medial and truncation on k-orbit maps and use them in classifying 2-orbit and 3-orbit maps on surfaces of small genus. |
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| Keywords: | Maps Monodromy groups Medials of maps Truncations of maps Polyhedra k-Orbit maps |
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