alexa Balanced Folding Over a Polygon and Euler Numbers

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Balanced Folding Over a Polygon and Euler Numbers

A cellular folding f: K→L is neat if Ln - Ln-1 consists of a single n-cell, interior L. The set of all cellular folding of K into L is denoted by C(K, L) and the set of all neat foldings of K into L by (K, L). If f ∈ C(K, L), then x∈K is said to be a singularity of f iff f is not a local homeomorphism at x. The set of all singularities of f corresponds to the "folds" of the map. This set associates a cell decomposition Cf of M. If M is a surface, then the edges and vertices of Cf form a graph Γf embedded in M.

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