Partial duality of hypermaps

2014/09/02 by Chmutov, Sergei, Vignes-Tourneret, Fabien
#05C10 #05C65 #57M15 #57Q15 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1409.0632

Abstract

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 τ-model), or as three permutations on the set of half-edges (rotation system or σ-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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