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Article Dans Une Revue Arnold Mathematical Journal Année : 2022

Partial duality of hypermaps

Résumé

We introduce partial duality of hypermaps, which include the classical Euler-Poincaré duality as a particular case. Combinatorially, hypermaps may be described in one of three ways: as three involutions on the set of flags (bi-rotation system or $\tau$-model), or as three permutations on the set of half-edges (rotation system or $\sigma$-model in orientable case), or as edge 3-coloured graphs. We express partial duality in each of these models. We give a formula for the genus change under partial duality.

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Dates et versions

hal-01060262 , version 1 (15-02-2019)
hal-01060262 , version 2 (18-11-2021)

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Sergei Chmutov, Fabien Vignes-Tourneret. Partial duality of hypermaps. Arnold Mathematical Journal, 2022, ⟨10.1007/s40598-021-00194-8⟩. ⟨hal-01060262v2⟩
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