The work is devoted to extend to dimension five the following combinatorial characterization of (orientable and non-orientable) handlebodies, already proved for dimensions three and four by the same author: a compact connected 5-manifold $M^5$ is a handlebody (of genus g) iff $ G(M^5)= G(\partial M^5} (=g)$, $G(X) being the regular genus of the manifold X. Moreover, partial results in dimension n induce to conjecture that an analogous characterization also holds for handlebodies of arbitrary dimension.
A note on the characterization of handlebodies / Casali, Maria Rita. - In: EUROPEAN JOURNAL OF COMBINATORICS. - ISSN 0195-6698. - STAMPA. - 14:(1993), pp. 301-310. [10.1006/eujc.1993.1033]