A Note on the Characterization of Handlebodies

This 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 in [2] and [3]: a compact connected 5-manifold M 5 is a handlebody (of genus g) iff G ̈ ( M 5) = G ̈ (∂ M 5)(= g), G ̈ ( X) being the regular genus of the manifold X. Moreover, partial results in dimension n induce the conjecture that an analogous characterization also holds for handlebodies of arbitrary dimension.