Regular genus: the boundary case
A particular kind of 2-cell imbedding for a class of edge-coloured graphs into surfaces with boundary is introduced and studied. This allows one to define, as in our earlier work [Proc. Am. Math. Soc. 81, 473-481 (1981; Zbl 0467.57004)], where the closed case was treated, a pair of invariants - the regular genus and the hole-number - for every n-manifold with boundary. These invariants are proved to coincide with the classical ones in dimension two, and to be strictly related with a Heegaard-like handlebody decomposition in dimension three. A characterization of \({\mathbb{D}}^ n\) concludes the work.
scientific article; zbMATH DE number 4003076