Paola Bandieri

NON-ORIENTABLE 3-MANIFOLDS ADMITTING COLORED TRIANGULATIONS WITH AT MOST 30 TETRAHEDRA

We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid non-bipartite crystallizations up to 30 vertices.

A census of genus-two 3-manifolds up to 42 coloured tetrahedra

We improve and extend to the non-orientable case a recent result of Karabas, Malicky and Nedela concerning the classification of all orientable prime 3-manifolds of Heegaard genus two, triangulated with at most 42 coloured tetrahedra.

Combinatorial handles and manifolds with boundary

In this work we complete the study ofcombinatorial handles in (n+1)-coloured graphs with boundary, introduced in [G1], [L] and [GV] for graphs with empty boundary and in [BGV] for 3-coloured graphs with boundary. In particular, we study the cancelling of a combinatorial handle from an (n+1)-coloured graph and its effects on the associated complex.

Representing products of manifolds by edge-coloured graphs: the boundary case

Abstract. In this paper we generalize the construction - introduced by Gagliardi and Grasselli in the closed case - of a coloured-graph representing the product of two manifolds, starting by two coloured graphs representing the manifolds themselves, to the boundary case. In particular we study the genus of the graph product of low dimensional manifold ( resp. n-spheres ) with m-disks.

Contracted k -tessellations of closed surfaces

Abstract In this paper we study tilings of closed surfaces by means of polygons with k edges, which are minimal with respect to the number of vertices.

A note on the genus of 3-manifolds with boundary

SummaryIn this paper we prove that the minimum among all regular genera of the graphs representing a 3-manifold with boundaryM3 can always be obtained by a crystallization. As a consequence, we also prove that every 3-coloured graph representing ∂M3 is the boundary of a 4-coloured graph which representsM3 and whose genus equals the regular genus ofM3.RiassuntoIn questo lavoro si prova che ogni 3-varietà con bordoM3 ammette sempre una cristallizzazione di genere minimo. Come conseguenza, si ottiene che ogni grafo 3-colorato che rappresenta ∂M3 è il bordo di un grafo 4-colorato che rappresentaM3, il cui genere è uguale al genere regolare diM3.