Combinatorial Oriented Maps

Publisher Website
Google Scholar
Abstract
An orientable map is often presented as a realization of a finite connected graphGin an orientable surface so that the complementary domains ofG, the “faces” of the map are topological open discs. This is not the definition to be used in the paper. But let us contemplate it for a while.On each edge ofGwe can recognize two opposite directed edges, or “darts”. Letθbe the permutation of the dart-setSthat interchanges each dart with its opposite. The darts radiating from a vertexvoccur in a definite cyclic order, fixed by a chosen positive sense of rotation on the surface. The cyclic orders at the various vertices are the cycles of a permutationPofS. The choice ofPrather thanP–l, which corresponds to the other sense of rotation, makes the map “oriented”.

This publication has 0 references indexed in Scilit: