Some graph-theoretical tools are used to introduce the concept of "regular genus" §(M "), for every closed n-dimensional PL-manifold M ". Then it is proved that the regular genus of every surface equals its genus, and that the regular genus of every 3-manifold Af j equals its Heegaard genus, if M3 is orientable, and twice its Heegaard genus, if M3 is… (More)
We improve and extend to the non-orientable case a recent result of Karabas, Malicki and Nedela concerning the classification of all orientable prime 3-manifolds of Heegaard genus two, triangulated with at most 42 coloured tetrahedra.
All n-manifolds of regular genus zero, i.e. admitting a crystallization which regularly imbeds into S2, are proved to be homeomorphic to S". A conjecture implying the Poincaré Conjecture in dimension four is also formulated. Sunto. Si dimostra che tutte le /i-varietà di genere regolare zero, cioè aventi una cristallizzazione che si immerge regolarmente in… (More)